https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Amzimmer2&feedformat=atomUW-Math Wiki - User contributions [en]2024-03-29T10:26:38ZUser contributionsMediaWiki 1.39.5https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=26362Group Actions and Dynamics Seminar2024-03-25T20:01:35Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|January 24 (1pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|Unique Equilibrium States for Geodesic Flows<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|Geometric Boundary of Groups<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|Divisible convex sets in flag manifolds and rigidity<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|Equidistribution of twist tori<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|Shrinking targets on square-tiled surfaces<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://www.caglaruyanik.com Caglar Uyanik] (UW)<br />
|Cannon-Thurston maps, random walks, and rigidity<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://math.indiana.edu/about/faculty/bainbridge-matt.html Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|<br />
|-<br />
|September 23<br />
|[http://www.harrisonbray.com/ Harrison Bray] (George Mason)<br />
|TBA<br />
|Zimmer<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
<br />
In this talk I will discuss some known results about the geodesics and equilibrium states of the geodesic flow in negative curvature. After, I will introduce some of the tools and techniques needed to show the uniqueness of equilibrium states in the setting of translation surfaces. If time allows, I will talk about some of our upcoming work about the Bernoulli property. This is joint work with Benjamin Call, Dave Constantine, Alena Erchenko, and Grace Work. <br />
===Yulan Qing===<br />
<br />
Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk. <br />
<br />
The sublinearly Morse boundaries are subsets of all directions with desired properties. In the second half of the talk, we will truly consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries are embedded. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.<br />
<br />
===Blandine Galiay===<br />
<br />
Divisible convex sets have been widely studied since the 1960s. They are proper domains of the projective space that admit a cocompact action of a discrete subgroup of the linear projective group. The best-known examples are symmetric spaces embedded in the projective space, but there are also many nonsymmetric examples. It is natural to seek to generalize this theory, by replacing the projective space by a flag variety G/P, where G is a real semisimple non-compact Lie group and P a parabolic of G. A question of van Limbeek and Zimmer is then: are there examples of divisible convex sets in G/P that are nonsymmetric? In a number of cases, it has been proved that there are not. In this talk, we will focus on some particular classes of flag varieties in which rigidity can indeed be observed.<br />
<br />
===David Aulicino===<br />
<br />
We consider generic translation surfaces of genus g>0 with marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order d. Given a translation surface, the number of cylinders with waist curve of length at most L grows like L^2. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by L^2, the limit as L goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points n. All necessary background will be given and a connection to combinatorics will be presented. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.<br />
<br />
===Aaron Calderon===<br />
Given a hyperbolic surface and a collection of simple closed geodesics, one can build a family of related metrics by cutting open the surface and twisting along the geodesics. This creates to an immersed ``twist torus’’ inside the moduli space of hyperbolic structures, which turns out to be a minimal set for the unipotent-like "earthquake flow." Maryam Mirzakhani famously asked if these twist tori equidistribute when pushed forward under a corresponding geodesic(-like) flow; in this talk, I will explain joint work with James Farre in which we prove that they do equidistribute in some cases, and that they do not in others. The key tool is a bridge that allows for the transfer of ergodic-theoretic results between flat and hyperbolic geometry.<br />
<br />
===Josh Southerland===<br />
<br />
In this talk, we will study a shrinking target problem for square-tiled surfaces. A square-tiled surface is a type of translation surface which arises as a branched cover of the torus (branched over one point). The moduli space of translation surfaces carries an action of $SL^+_2(\R)$, and the stabilizer of this action is called the Veech group. We will show that the action of a subgroup of the Veech group of a square-tiled surface exhibits Diophantine-like properties. This generalizes the work of Finkelshtein, who studied a similar problem on the torus. <br />
<br />
===Caglar Uyanik===<br />
<br />
Cannon and Thurston showed that a hyperbolic 3-manifold that fibers over the circle gives rise to a sphere-filling curve. The universal cover of the fiber surface is quasi-isometric to the hyperbolic plane, whose boundary is a circle, and the universal cover of the 3-manifold is 3-dimensional hyperbolic space, whose boundary is the 2-sphere. Cannon and Thurston showed that the inclusion map between the universal covers extends to a continuous map between their boundaries, whose image is dense. In particular, any measure on the circle pushes forward to a measure on the 2-sphere using this map. We compare several natural measures coming from this construction. This is joint work with Gadre, Haettel, Maher, and Pfaff.<br />
<br />
<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=26361Group Actions and Dynamics Seminar2024-03-25T20:01:17Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|January 24 (1pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|Unique Equilibrium States for Geodesic Flows<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|Geometric Boundary of Groups<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|Divisible convex sets in flag manifolds and rigidity<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|Siegel-Veech Constants of Cyclic Covers of Generic Translation Surfaces<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|Equidistribution of twist tori<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|Shrinking targets on square-tiled surfaces<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://www.caglaruyanik.com Caglar Uyanik] (UW)<br />
|Cannon-Thurston maps, random walks, and rigidity<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://math.indiana.edu/about/faculty/bainbridge-matt.html Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|<br />
|-<br />
|September 23<br />
|[http://www.harrisonbray.com/ Harrison Bray] ()<br />
|TBA<br />
|Zimmer<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
<br />
In this talk I will discuss some known results about the geodesics and equilibrium states of the geodesic flow in negative curvature. After, I will introduce some of the tools and techniques needed to show the uniqueness of equilibrium states in the setting of translation surfaces. If time allows, I will talk about some of our upcoming work about the Bernoulli property. This is joint work with Benjamin Call, Dave Constantine, Alena Erchenko, and Grace Work. <br />
===Yulan Qing===<br />
<br />
Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk. <br />
<br />
The sublinearly Morse boundaries are subsets of all directions with desired properties. In the second half of the talk, we will truly consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries are embedded. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.<br />
<br />
===Blandine Galiay===<br />
<br />
Divisible convex sets have been widely studied since the 1960s. They are proper domains of the projective space that admit a cocompact action of a discrete subgroup of the linear projective group. The best-known examples are symmetric spaces embedded in the projective space, but there are also many nonsymmetric examples. It is natural to seek to generalize this theory, by replacing the projective space by a flag variety G/P, where G is a real semisimple non-compact Lie group and P a parabolic of G. A question of van Limbeek and Zimmer is then: are there examples of divisible convex sets in G/P that are nonsymmetric? In a number of cases, it has been proved that there are not. In this talk, we will focus on some particular classes of flag varieties in which rigidity can indeed be observed.<br />
<br />
===David Aulicino===<br />
<br />
We consider generic translation surfaces of genus g>0 with marked points and take covers branched over the marked points such that the monodromy of every element in the fundamental group lies in a cyclic group of order d. Given a translation surface, the number of cylinders with waist curve of length at most L grows like L^2. By work of Veech and Eskin-Masur, when normalizing the number of cylinders by L^2, the limit as L goes to infinity exists and the resulting number is called a Siegel-Veech constant. The same holds true if we weight the cylinders by their area. Remarkably, the Siegel-Veech constant resulting from counting cylinders weighted by area is independent of the number of branch points n. All necessary background will be given and a connection to combinatorics will be presented. This is joint work with Aaron Calderon, Carlos Matheus, Nick Salter, and Martin Schmoll.<br />
<br />
===Aaron Calderon===<br />
Given a hyperbolic surface and a collection of simple closed geodesics, one can build a family of related metrics by cutting open the surface and twisting along the geodesics. This creates to an immersed ``twist torus’’ inside the moduli space of hyperbolic structures, which turns out to be a minimal set for the unipotent-like "earthquake flow." Maryam Mirzakhani famously asked if these twist tori equidistribute when pushed forward under a corresponding geodesic(-like) flow; in this talk, I will explain joint work with James Farre in which we prove that they do equidistribute in some cases, and that they do not in others. The key tool is a bridge that allows for the transfer of ergodic-theoretic results between flat and hyperbolic geometry.<br />
<br />
===Josh Southerland===<br />
<br />
In this talk, we will study a shrinking target problem for square-tiled surfaces. A square-tiled surface is a type of translation surface which arises as a branched cover of the torus (branched over one point). The moduli space of translation surfaces carries an action of $SL^+_2(\R)$, and the stabilizer of this action is called the Veech group. We will show that the action of a subgroup of the Veech group of a square-tiled surface exhibits Diophantine-like properties. This generalizes the work of Finkelshtein, who studied a similar problem on the torus. <br />
<br />
===Caglar Uyanik===<br />
<br />
Cannon and Thurston showed that a hyperbolic 3-manifold that fibers over the circle gives rise to a sphere-filling curve. The universal cover of the fiber surface is quasi-isometric to the hyperbolic plane, whose boundary is a circle, and the universal cover of the 3-manifold is 3-dimensional hyperbolic space, whose boundary is the 2-sphere. Cannon and Thurston showed that the inclusion map between the universal covers extends to a continuous map between their boundaries, whose image is dense. In particular, any measure on the circle pushes forward to a measure on the 2-sphere using this map. We compare several natural measures coming from this construction. This is joint work with Gadre, Haettel, Maher, and Pfaff.<br />
<br />
<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=26193Group Actions and Dynamics Seminar2024-02-22T19:27:53Z<p>Amzimmer2: /* Spring Abstracts */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|January 24 (1pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|Unique Equilibrium States for Geodesic Flows<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|Geometric Boundary of Groups<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|Divisible convex sets in flag manifolds and rigidity<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://www.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
<br />
In this talk I will discuss some known results about the geodesics and equilibrium states of the geodesic flow in negative curvature. After, I will introduce some of the tools and techniques needed to show the uniqueness of equilibrium states in the setting of translation surfaces. If time allows, I will talk about some of our upcoming work about the Bernoulli property. This is joint work with Benjamin Call, Dave Constantine, Alena Erchenko, and Grace Work. <br />
<br />
<br />
<br />
===Yulan Qing===<br />
<br />
Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk. <br />
<br />
The sublinearly Morse boundaries are subsets of all directions with desired properties. In the second half of the talk, we will truly consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries are embedded. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.<br />
<br />
===Blandine Galiay===<br />
<br />
Divisible convex sets have been widely studied since the 1960s. They are proper domains of the projective space that admit a cocompact action of a discrete subgroup of the linear projective group. The best-known examples are symmetric spaces embedded in the projective space, but there are also many nonsymmetric examples. It is natural to seek to generalize this theory, by replacing the projective space by a flag variety G/P, where G is a real semisimple non-compact Lie group and P a parabolic of G. A question of van Limbeek and Zimmer is then: are there examples of divisible convex sets in G/P that are nonsymmetric? In a number of cases, it has been proved that there are not. In this talk, we will focus on some particular classes of flag varieties in which rigidity can indeed be observed.<br />
<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=26192Group Actions and Dynamics Seminar2024-02-22T19:27:13Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|January 24 (1pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|Unique Equilibrium States for Geodesic Flows<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|Geometric Boundary of Groups<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|Divisible convex sets in flag manifolds and rigidity<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://www.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
<br />
In this talk I will discuss some known results about the geodesics and equilibrium states of the geodesic flow in negative curvature. After, I will introduce some of the tools and techniques needed to show the uniqueness of equilibrium states in the setting of translation surfaces. If time allows, I will talk about some of our upcoming work about the Bernoulli property. This is joint work with Benjamin Call, Dave Constantine, Alena Erchenko, and Grace Work. <br />
<br />
<br />
<br />
===Yulan Qing===<br />
<br />
Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk. <br />
<br />
The sublinearly Morse boundaries are subsets of all directions with desired properties. In the second half of the talk, we will truly consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries are embedded. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.<br />
<br />
===Blandine Galiay===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=26106Group Actions and Dynamics Seminar2024-02-12T17:03:52Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|January 24 (1pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|Unique Equilibrium States for Geodesic Flows<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|Geometric Boundary of Groups<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://www.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
<br />
In this talk I will discuss some known results about the geodesics and equilibrium states of the geodesic flow in negative curvature. After, I will introduce some of the tools and techniques needed to show the uniqueness of equilibrium states in the setting of translation surfaces. If time allows, I will talk about some of our upcoming work about the Bernoulli property. This is joint work with Benjamin Call, Dave Constantine, Alena Erchenko, and Grace Work. <br />
<br />
<br />
<br />
===Yulan Qing===<br />
<br />
Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk. <br />
<br />
The sublinearly Morse boundaries are subsets of all directions with desired properties. In the second half of the talk, we will truly consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries are embedded. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.<br />
<br />
===Blandine Galiay===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=26105Group Actions and Dynamics Seminar2024-02-12T17:03:33Z<p>Amzimmer2: /* Yulan Qing */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|January 24 (1pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|Unique Equilibrium States for Geodesic Flows<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://www.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
<br />
In this talk I will discuss some known results about the geodesics and equilibrium states of the geodesic flow in negative curvature. After, I will introduce some of the tools and techniques needed to show the uniqueness of equilibrium states in the setting of translation surfaces. If time allows, I will talk about some of our upcoming work about the Bernoulli property. This is joint work with Benjamin Call, Dave Constantine, Alena Erchenko, and Grace Work. <br />
<br />
<br />
<br />
===Yulan Qing===<br />
<br />
Gromov boundary provides a useful compactification for all infinite-diameter Gromov hyperbolic spaces. It consists of all geodesic rays starting at a given base-point and it is an essential tool in the study of the coarse geometry of hyperbolic groups. In this talk we generalize the Gromov boundary. We first construct the sublinearly Morse boundaries and show that it is a QI-invariant, metrizable topological space. We show sublinearly Morse directions are generic both in the sense of Patterson-Sullivan and in the sense of random walk. <br />
<br />
The sublinearly Morse boundaries are subsets of all directions with desired properties. In the second half of the talk, we will truly consider the space of all directions and show that with some minimal assumptions on the space, the resulting boundary is a QI-invariant topology space in which many existing boundaries are embedded. This talk is based on a series of work with Kasra Rafi and Giulio Tiozzo.<br />
<br />
===Blandine Galiay===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Whatcha_Doing_Seminar&diff=26046Whatcha Doing Seminar2024-02-05T16:27:41Z<p>Amzimmer2: </p>
<hr />
<div>The Whatcha Doin' Seminar is a place where professors can give 20-30 minute talks about their research aimed at beginning graduate students. This will give students an opportunity to meet potential advisors and see what they are up to.<br />
<br />
Time: '''Mondays''' '''4:00PM-4:30PM'''<br />
<br />
Location: '''Van Vleck B317'''<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |research area<br />
! align="left" |title<br />
|-<br />
|January 29<br />
|<br />
|<br />
|<br />
|-<br />
|February 5<br />
|<br />
|<br />
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|-<br />
|February 12<br />
|<br />
|<br />
|<br />
|-<br />
|February 19<br />
|Autumn Kent<br />
|Geometry/Topology/Algebra<br />
|Moduli<br />
|-<br />
|February 26<br />
|<br />
|<br />
|<br />
|-<br />
|March 4<br />
|Andrew Zimmer<br />
|Dynamics/Analysis/Geometry/Topology/Algebra<br />
|Discrete subgroups of Lie groups<br />
|-<br />
|March 11<br />
|<br />
|<br />
|<br />
|-<br />
|March 18<br />
|<br />
|<br />
|<br />
|-<br />
|March 27<br />
|Spring Break<br />
|<br />
|<br />
|-<br />
|April 1<br />
|<br />
|<br />
|<br />
|-<br />
|April 8<br />
|<br />
|<br />
|<br />
|-<br />
|April 15<br />
|<br />
|<br />
|<br />
|-<br />
|April 22<br />
|<br />
|<br />
|<br />
|-<br />
|April 29<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
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<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |research area<br />
! align="left" |title<br />
|-<br />
|January 30<br />
|Jean-Luc Thiffeault<br />
|Applied Math<br />
|''Active matter''<br />
|-<br />
|February 6<br />
|Dima Arinkin<br />
|Algebraic geometry<br />
|''Formally, differential equations... actually, linear algebra''<br />
|-<br />
|February 13<br />
|Autumn Kent<br />
|Geometry and Topology<br />
|''Moduli'' <br />
|-<br />
|February 20<br />
|Tullia Dymarz<br />
|Geometry, Geometric Group Theory<br />
|Title<br />
|-<br />
|February 27<br />
|No seminar<br />
|<br />
|<br />
|-<br />
|March 6<br />
|Paul Apisa<br />
|Dynamics, geometry, topology<br />
|TBA<br />
|-<br />
|March 13<br />
|Spring Break, No Seminar<br />
|<br />
|<br />
|-<br />
|March 20<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|March 27<br />
|Sergey Denisov<br />
|Analysis & PDE<br />
|Title<br />
|-<br />
|April 3<br />
|Andrew Zimmer<br />
|TBA<br />
|TBA<br />
|-<br />
|April 10<br />
|No seminar<br />
|<br />
|Title<br />
|-<br />
|April 17<br />
|<br />
|<br />
|Title<br />
|-<br />
||April 24<br />
|Chenxi Wu<br />
|Dynamics<br />
|Title<br />
|-<br />
|May 1<br />
|Marissa Loving<br />
|Geometry, topology, and dynamics<br />
|TBA<br />
|-<br />
|}</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=25960Group Actions and Dynamics Seminar2024-01-23T16:03:31Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Dymarz and Uyanik<br />
|<br />
|-<br />
|January 24 (1pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|TBA<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://wwww.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
===Yulan Qing===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=25940Group Actions and Dynamics Seminar2024-01-19T16:46:14Z<p>Amzimmer2: /* Mitul Islam */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Dymarz and Uyanik<br />
|<br />
|-<br />
|January 24 (2:30pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|TBA<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://wwww.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
<br />
The (Hilbert metric) geometry of properly convex domains generalizes real hyperbolic geometry. This generalization is far from the Riemannian notion of non-positive curvature, but they have some intriguing similarities. I will explore this connection from a coarse geometry viewpoint.<br />
The focus will be on Morse geodesics ("negatively curved directions", in a coarse sense) in properly convex domains. I will show that Morse-ness can be characterized entirely using linear algebraic data (i.e. singular values of matrices that track the geodesic). Further, I will discuss how this coarse geometric notion of Morse is related to the symmetric space geometry as well as the smoothness of boundary points. This is joint work with Theodore Weisman.<br />
<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
===Yulan Qing===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=25939Group Actions and Dynamics Seminar2024-01-19T16:46:01Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Dymarz and Uyanik<br />
|<br />
|-<br />
|January 24 (2:30pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|Morse-ness in convex projective geometry<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|TBA<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://wwww.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
===Yulan Qing===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=25938Group Actions and Dynamics Seminar2024-01-19T16:44:35Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Dymarz and Uyanik<br />
|<br />
|-<br />
|January 24 (2:30pm in VV 901)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|TBA<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://wwww.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
===Yulan Qing===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=25917Group Actions and Dynamics Seminar2024-01-17T21:50:29Z<p>Amzimmer2: /* Michael Zshornack */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Dymarz and Uyanik<br />
|<br />
|-<br />
|January 24 (SPECIAL TIME/PLACE)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|TBA<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://wwww.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
===Michael Zshornack===<br />
<br />
Margulis's work on lattices in higher-rank and a number of questions on the existence of surface subgroups motivate the need for understanding arithmetic properties of spaces of surface group representations. In recent work with Jacques Audibert, we outline one possible approach towards understanding such properties for the Hitchin component, one particularly nice space of representations. We utilize the underlying geometry of this space to reduce questions about its arithmetic to questions about the arithmetic of certain algebraic groups, which in turn, allows us to characterize the rational points on these components. In this talk, I'll give an overview of the geometric methods behind the proof of our result and indicate some natural questions about the nature of the resulting surface group actions that follow.<br />
<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
===Yulan Qing===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=25916Group Actions and Dynamics Seminar2024-01-17T21:48:57Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Dymarz and Uyanik<br />
|<br />
|-<br />
|January 24 (SPECIAL TIME/PLACE)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|Rational surface groups on the Hitchin component<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|TBA<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://wwww.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
===Michael Zshornack===<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
===Yulan Qing===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=25915Group Actions and Dynamics Seminar2024-01-17T21:43:50Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Dymarz and Uyanik<br />
|<br />
|-<br />
|January 24 (SPECIAL TIME/PLACE)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|TBA<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|Blandine Galiay (IHES)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://wwww.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
===Mitul Islam===<br />
===Michael Zshornack===<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
===Yulan Qing===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Group_Actions_and_Dynamics_Seminar&diff=25900Group Actions and Dynamics Seminar2024-01-16T21:18:07Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>During the Spring 2024 semester, '''RTG / Group Actions and Dynamics''' seminar meets in room '''Sterling Hall 3425''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 22<br />
|[https://sites.google.com/view/aaron-messerla/ Aaron Messerla] (UIC)<br />
|Quasi-isometries of relatively hyperbolic groups with an elementary hierarchy<br />
|Dymarz and Uyanik<br />
|<br />
|-<br />
|January 24 (SPECIAL TIME/PLACE)<br />
|[https://mitul-islam.github.io/ Mitul Islam] (Max-Planck-Institut)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|Bootstrapping dynamics in the moduli space of non-orientable surfaces<br />
|Uyanik<br />
|<br />
|-<br />
|February 12<br />
|[https://www.noellesawyer.com Noelle Sawyer] (Southwestern)<br />
|TBA<br />
|Loving, Uyanik, Work<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 26<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|March 4<br />
|[http://userhome.brooklyn.cuny.edu/aulicino/ David Aulicino] (Brooklyn College)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|March 11<br />
|[https://aacalderon.com/ Aaron Calderon] (Chicago)<br />
|TBA<br />
|Loving and Uyanik<br />
|<br />
|-<br />
|March 18<br />
|[http://sub.mersion.cc Josh Southerland] (Indiana)<br />
|TBA<br />
|Fisher<br />
|<br />
|-<br />
|April 1<br />
|[http://wwww.caglaruyanik.com Caglar Uyanik] (UW)<br />
|TBA<br />
|local<br />
|<br />
|-<br />
|April 8<br />
|[https://mabainbr.pages.iu.edu/?_gl=1*r2jhoy*_ga*OTk3MTk0Mzg3LjE3MDQ5OTU1MTA.*_ga_61CH0D2DQW*MTcwNDk5NTYyMy4xLjAuMTcwNDk5NTYyMy42MC4wLjA.&_ga=2.157330302.532468181.1704995624-997194387.1704995510 Matt Bainbridge] (Indiana)<br />
|TBA<br />
|Apisa<br />
|<br />
|-<br />
|April 15<br />
|[https://math.hunter.cuny.edu/ilyakapo/ Ilya Kapovich] (CUNY)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|April 22<br />
|[https://sites.google.com/view/yuchanchang/ Yu-Chan Chang] (Wesleyan)<br />
|TBA<br />
|Dymarz<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Kent, Loving, Uyanik<br />
|}<br />
<br />
== Spring Abstracts ==<br />
===Aaron Messerla===<br />
<br />
Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. We prove that a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups, is closed under quasi-isometry. Additionally, these groups share some of the algebraic properties of limit groups. In this talk I plan to present motivation for and introduce the class of groups studied, as well as present some of the results for this class.<br />
<br />
===Michael Zshornack===<br />
===Sayantan Khan===<br />
<br />
The moduli spaces of non-orientable hyperbolic surfaces behave significantly differently from their orientable counterparts.<br />
They have infinite volume, almost all geodesic flow orbits escape off to infinity, and the growth of mapping class group orbit points and simple closed curves is believed to have non-integer exponents, unlike in the orientable setting.<br />
In this talk, we outline some of the oddities of these moduli spaces, and outline an approach for studying the dynamics on these spaces via Patterson-Sullivan theory.<br />
A key obstruction to imitating the techniques from the orientable setting is that a number of these techniques rely on the dynamics of the geodesic flow and the mapping class group action on Teichmüller spaces of orientable surfaces, which is not something we can do in the non-orientable setting, since that is what we are trying to prove.<br />
The way around these obstructions is by proving weaker versions of these dynamical statements using a dynamics free approach, which we then use to bootstrap the stronger results.<br />
<br />
===Noelle Sawyer===<br />
===Yulan Qing===<br />
===David Aulicino===<br />
===Aaron Calderon===<br />
===Josh Southerland===<br />
===Caglar Uyanik===<br />
===Matt Bainbridge===<br />
===Ilya Kapovich===<br />
===Yu-Chan Chang===<br />
===Chris Leininger===<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|Non-planarity of SL(2,Z)-orbits of origamis<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|Colloquium by [https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] at 4pm<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
Origamis (also known as square-tiled surfaces) arise naturally in a variety of settings in low-dimensional topology. They can be thought of as generalisations of the torus (the unit square with opposite sides glued) since they are surfaces obtained by gluing the opposite sides of a collection of unit squares. There is a natural action of the matrix group SL(2,Z) on origamis. In genus two (with some extra conditions) the orbits of this action were classified by Hubert-Lelièvre and McMullen. By considering a generating set of size two for SL(2,Z) and varying the number of squares used to build the origamis, we can turn these orbits into an infinite family of four-valent graphs. It is a long-standing conjecture of McMullen that these orbit graphs form a family of expander graphs. In this talk, giving indirect evidence for this conjecture, I will discuss joint work with Carlos Matheus in which we show that these orbit graphs are eventually non-planar - a requirement of any family of expander graphs.<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2024&diff=25714Colloquia/Spring20242023-12-16T16:03:02Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| Jan 19<br />
|<br />
|<br />
| <br />
|-<br />
| Jan 26<br />
|Jacob Bedrossian (UCLA)<br />
|<br />
|Tran<br />
|-<br />
| Feb 2<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 9<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 16<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 23<br />
|<br />
|<br />
|<br />
|-<br />
| Mar 1<br />
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
|TBA<br />
|Li<br />
|-<br />
| Mar 8<br />
|Anton Izosimov (U of Arizona)<br />
|<br />
|Gloria Mari-Beffa<br />
|-<br />
| Mar 15<br />
|<br />
|<br />
|<br />
|-<br />
|Mar 20<br />
|[https://www.math.wustl.edu/~wanlin/index.html Wanlin Li] (Washington U St Louis)<br />
|<br />
|Dymarz, GmMaW<br />
|-<br />
| Mar 22<br />
|[https://jacklutz.com/ Jack Lutz] (Iowa State)<br />
|<br />
|Guo<br />
|-<br />
| Mar 29<br />
|Spring break<br />
|<br />
|<br />
|-<br />
| Apr 5<br />
|[https://www.math.columbia.edu/~savin/ Ovidiu Savin] (Columbia)<br />
|<br />
|Tran<br />
|-<br />
|Apr 12<br />
|[https://www.mikaylakelley.com/about Mikayla Kelley] (U Chicago Philosophy)<br />
|Math And... seminar, title TBA<br />
|Ellenberg, Marshall<br />
<br />
|-<br />
| Apr 19<br />
|[https://sites.math.rutgers.edu/~yyli/ Yanyan Li] (Rutgers)<br />
|<br />
|Tran<br />
|-<br />
| Apr 26<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2024&diff=25709Colloquia/Spring20242023-12-14T17:00:01Z<p>Amzimmer2: /* Spring 2024 */</p>
<hr />
<div>== Spring 2024 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
| Jan 19<br />
|<br />
|<br />
| <br />
|-<br />
| Jan 26<br />
|Jacob Bedrossian (UCLA)<br />
|<br />
|Tran<br />
|-<br />
| Feb 2<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 9<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 16<br />
|<br />
|<br />
|<br />
|-<br />
| Feb 23<br />
|<br />
|<br />
|<br />
|-<br />
| Mar 1<br />
|[https://users.oden.utexas.edu/~pgm/ Per-Gunnar Martinsson] (UT-Austin)<br />
|TBA<br />
|Li<br />
|-<br />
| Mar 8<br />
|Anton Izosimov (U of Arizona)<br />
|<br />
|Gloria Mari-Beffa<br />
|-<br />
| Mar 15<br />
|TBA<br />
|<br />
|Zimmer<br />
|-<br />
|Mar 20<br />
|[https://www.math.wustl.edu/~wanlin/index.html Wanlin Li] (Washington U St Louis)<br />
|<br />
|Dymarz, GmMaW<br />
|-<br />
| Mar 22<br />
|[https://jacklutz.com/ Jack Lutz] (Iowa State)<br />
|<br />
|Guo<br />
|-<br />
| Mar 29<br />
|Spring break<br />
|<br />
|<br />
|-<br />
| Apr 5<br />
|[https://www.math.columbia.edu/~savin/ Ovidiu Savin] (Columbia)<br />
|<br />
|Tran<br />
|-<br />
|Apr 12<br />
|[https://www.mikaylakelley.com/about Mikayla Kelley] (U Chicago Philosophy)<br />
|Math And... seminar, title TBA<br />
|Ellenberg, Marshall<br />
<br />
|-<br />
| Apr 19<br />
|[https://sites.math.rutgers.edu/~yyli/ Yanyan Li] (Rutgers)<br />
|<br />
|Tran<br />
|-<br />
| Apr 26<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar&diff=25622Dynamics Seminar2023-11-21T13:52:41Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>During the Fall 2023 semester, '''RTG / Group Actions and [[Dynamics]]''' seminar meets in room '''Sterling Hall 1339''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
| A metric view of polynomial shift locus<br />
|Wu<br />
|-<br />
|November 20<br />
||[https://sfreedman67.github.io/ Sam Freedman] (Brown)<br />
|Periodic points of Prym eigenforms<br />
|Apisa<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|TBA<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
The escaping rates of critical points for polynomials in C[z] induce a continuous and proper map on the moduli space M_d of degree d\ge 2 polynomials. This map has a monotone-light factorization via an intermediate space T_d^* studied by DeMarco and Pilgrim. Restricting on the shift locus S_d of M_d, one obtains the corresponding intermediate space ST_d^*. In this talk, I will relate generic points in S_d to the length functions on the (2d-2)-rose graph and then present an understanding of the natural projectivization of ST_d^* from a metric view. The metric is obtained from thermodynamic metrics on the space of metric graphs. This is a joint work with Yan Mary He.<br />
<br />
===Sam Freedman===<br />
<br />
We will consider the dynamics of affine automorphisms acting on highly symmetric translation surfaces called Veech surfaces. Specifically, we’ll examine the points of the surface that are periodic, i.e., have a finite orbit under the whole automorphism group. While this set is known to be finite for primitive Veech surfaces, for applications it is desirable to determine the periodic points explicitly. In this talk we will discuss our classification of periodic points in the case of minimal Prym eigenforms, certain primitive Veech surfaces in genera 2, 3, and 4.<br />
<br />
===Luke Jeffreys===<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
== Spring 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|February 5<br />
|[https://www.sayantankhan.io Sayantan Khan] (Michigan)<br />
|TBA<br />
|Uyanik<br />
|<br />
|-<br />
|February 19<br />
|[https://web.math.utk.edu/~yqing/ Yulan Qing] (Tennessee)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar&diff=25541Dynamics Seminar2023-11-06T21:11:18Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>During the Fall 2023 semester, '''RTG / Group Actions and [[Dynamics]]''' seminar meets in room '''Sterling Hall 1339''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
|TBA<br />
|Wu<br />
|-<br />
|November 20<br />
|No seminar<br />
|<br />
|<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|TBA<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
===Luke Jeffreys===<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
== Spring 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|TBA<br />
|Zimmer<br />
|<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar&diff=25540Dynamics Seminar2023-11-06T21:10:47Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>During the Fall 2023 semester, '''RTG / Group Actions and [[Dynamics]]''' seminar meets in room '''Sterling Hall 1339''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
|TBA<br />
|Wu<br />
|-<br />
|November 20<br />
|No seminar<br />
|<br />
|<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|TBA<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
===Luke Jeffreys===<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
== Spring 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|TBA<br />
|Zimmer<br />
<br />
<br />
<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar&diff=25539Dynamics Seminar2023-11-06T21:10:27Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>During the Fall 2023 semester, '''RTG / Group Actions and [[Dynamics]]''' seminar meets in room '''Sterling Hall 1339''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
|TBA<br />
|Wu<br />
|-<br />
|November 20<br />
|No seminar<br />
|<br />
|<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|TBA<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
===Luke Jeffreys===<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
== Spring 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|TBA<br />
|Zimmer<br />
<br />
<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar&diff=25538Dynamics Seminar2023-11-06T21:10:17Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>During the Fall 2023 semester, '''RTG / Group Actions and [[Dynamics]]''' seminar meets in room '''Sterling Hall 1339''' on '''Mondays''' from '''2:25pm - 3:15pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
== Fall 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 11<br />
|[https://www.maths.gla.ac.uk/~vgadre/ Vaibhav Gadre] (Glasgow)<br />
|Teichmuller flow detects the fundamental group<br />
|Apisa<br />
|<br />
|-<br />
|September 18<br />
|[https://sites.google.com/view/beckyeastham/ Becky Eastham] (UW Madison)<br />
|Whitehead space: a tool to study finite regular covers of graphs<br />
|local<br />
|-<br />
|September 25<br />
|[https://sites.google.com/view/algebrandis/ Brandis Whitfield] (Temple)<br />
|Short curves of end-periodic mapping tori<br />
|Loving<br />
|-<br />
|September 28 '''(Thursday 4-5pm in B139)'''<br />
|[https://sites.google.com/view/itamarv/home Itamar Vigdorovich] (Weizmann)<br />
|Group stability, characters, and dynamics on compact groups<br />
|Dymarz/Gurevich<br />
|-<br />
|October 2<br />
|[https://hanhv.github.io/ Hanh Vo] (Arizona State)<br />
|Short geodesics with self-intersections<br />
|Dymarz<br />
|-<br />
|October 9<br />
|[https://people.math.wisc.edu/~ywu495/ Yandi Wu] (UW Madison)<br />
|Marked Length Spectrum Rigidity for Surface Amalgams<br />
|local<br />
|-<br />
|October 16<br />
|[https://www.samkwak.info/ Sanghoon Kwak] (Utah)<br />
|Mapping class groups of Infinite graphs — “Big Out(Fn)”<br />
|Loving<br />
|-<br />
|October 23 '''(11:55-12:55 in B223)'''<br />
|[https://sites.google.com/view/sara-maloni Sara Maloni] (UVA)<br />
|Dynamics on the SU(2,1)-character varieties of the one-holed torus<br />
|Uyanik<br />
|-<br />
|October 30<br />
|[http://www.math.toronto.edu/tiozzo/ Giulio Tiozzo] (Toronto)<br />
|A characterization of hyperbolic groups via contracting elements<br />
|Uyanik<br />
|-<br />
|November 6<br />
|<br />
|<br />
|<br />
|-<br />
<br />
|November 13<br />
|[https://sites.google.com/view/hmnie/home Hongming Nie] (Stony Brook)<br />
|TBA<br />
|Wu<br />
|-<br />
|November 20<br />
|No seminar<br />
|<br />
|<br />
|-<br />
|November 27<br />
|[https://people.math.wisc.edu/~ljeffreys/ Luke Jeffreys] (UW Madison)<br />
|TBA<br />
|local<br />
|-<br />
|December 4<br />
|[http://www.estark.net/ Emily Stark] (Wesleyan)<br />
|Graphically discrete groups and rigidity<br />
|Uyanik<br />
|-<br />
|December 11<br />
|<br />
|<br />
|<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Vaibhav Gadre===<br />
<br />
A quadratic differential on a Riemann surface is equivalent to a half-translation structure on the surface by complex charts with half-translation transitions. The SL(2,R)-action on the complex plane takes half-translations to half-translations and so descends to moduli spaces of quadratic differentials. The diagonal part of the action is the Teichmuller flow. <br />
<br />
<br />
Apart from its intrinsic interest, the dynamics of Teichmuller flow is central to many applications in geometry, topology and dynamics. The Konstevich—Zorich cocycle which records the action of the flow on the absolute homology of the surface, plays a key role.<br />
<br />
<br />
In this talk, I will explain how the flow detects the topology of moduli spaces. Specifically, we will show that the flow group, namely the subgroup generated by almost flow loops, has finite index in the fundamental group. As a corollary, we will prove that the minus and plus (modular) Rauzy—Veech groups have finite index in the fundamental group, answering a question by Yoccoz.<br />
<br />
<br />
Using this, and Filip’s results on algebraic hulls and Zariski closures of modular monodromies, we prove that the Konstevich—Zurich cocycle (separately minus and plus pieces) have a simple Lyapunov spectrum, extending the work of Forni from 2002 and Avila—Viana from 2007.<br />
<br />
===Becky Eastham===<br />
<br />
The Whitehead space of a finite regular cover of the rose is a locally infinite graph whose vertices are in one-to-one correspondence with conjugacy classes of elements of the subgroup associated with the cover. Every Whitehead space is a subgraph of the quotient of <math>\mathrm{Cay}(F_n, \mathcal{C})</math> by conjugacy; here $\mathcal{C}$ is the set of elements of $F_n$ conjugate into a proper free factor. Our main interest in this space is that it is connected if and only if the fundamental group of the associated cover is generated by lifts of elements of $\mathcal{C}$ to the cover. In addition, Whitehead space of the rose is an infinite-diameter, non-hyperbolic, one-ended space with an isometric action of $\mathrm{Out}(F_n)$. Thus, Whitehead space is not quasi-isometric to the free factor complex, the free splitting complex, or Outer Space.<br />
<br />
===Brandis Whitfield===<br />
Let $S$ be a boundaryless infinite-type surface with finitely many ends and consider an end-periodic homeomorphism $f$$ $of S. The end-periodicity of $f$ ensures that $M_f$, its associated mapping torus, has a compactification as a $3$-manifold with boundary; and further, if $f$ is atoroidal, then $M_f$ admits a hyperbolic metric.<br />
<br />
As an end-periodic analogy to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.<br />
<br />
In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic $3$-manifolds, and how these techniques may be used in the infinite-type setting.<br />
<br />
===Itamar Vigdorovich===<br />
<br />
I will discuss three seemingly unrelated topics:<br />
1. Stability: given a pair of matrices that almost commute, can they be perturbed to matrices which do commute? Interestingly, the answer highly depends on the chosen metric on matrices. This question is a special case of group stability: is every almost-homomorphism close to an actual homomorphism?<br />
2. Characters: these are functions on groups with special properties that generalize the classical notion in Pontryagin's theory of abelian groups, and in Frobenius's theory of finite groups. Is every character a limit of a finite-dimensional character?<br />
3. Topological dynamics: given a group G acting by homeomorphisms on a compact space X, are the periodic measures dense is the space all invariant measures?<br />
In this talk I will present these three subjects of study and explain how there are all in fact intimately related, as least in the amenable setting. For example, stability of the lamplighter group is strongly related to the orbit closing lemma for the Bernoulli shift, and stability of the semidirect product ZxZ[1/6] is related to whether Furstenberg's x2x3 system has dense periodic measures. <br />
The talk is based on a joint work with Arie Levit.<br />
<br />
===Hanh Vo===<br />
<br />
We consider the set of closed geodesics on a hyperbolic surface. Given any non-negative integer k, we are interested in the set of primitive essential closed geodesics with at least k self-intersections. Among these, we investigate those of minimal length. In this talk, we will discuss their self-intersection numbers.<br />
<br />
===Yandi Wu===<br />
<br />
The marked length spectrum of a negatively curved metric space can be thought of as a length assignment to every closed geodesic in the space. A celebrated result by Otal says that metrics on negatively curved closed surfaces are determined completely by their marked length spectra. In my talk, I will discuss my work towards extending Otal’s result to a large class of surface amalgams, which are natural generalizations of surfaces.<br />
<br />
===Sanghoon Kwak===<br />
Surfaces and graphs are closely related; there are many parallels between the mapping class groups of finite-type surfaces and finite graphs, where the mapping class group of a finite graph is the outer automorphism group of a free group of (finite) rank. A recent surge of interest in infinite-type surfaces and their mapping class groups begs a natural question: What is the mapping class group of an “infinite” graph? In this talk, I will explain the answer given by Algom-Kfir and Bestvina and present recent work, joint with George Domat (Rice University), and Hannah Hoganson (University of Maryland), on the coarse geometry of such groups.<br />
<br />
===Sara Maloni===<br />
<br />
In this talk we will discuss join work in progress with S. Lawton and F. Palesi on the (relative) SU(2, 1)–character variety for the once-holed torus. We consider the action of the mapping class group and describe a domain of discontinuity for this action, which strictly contains the set of convex-cocompact characters. We will also discuss the connection with the recent work of S. Schlich, and the inspiration behind this project, which lies in the rich theory developed for SL(2, C)–character varieties by Bowditch, Minsky and others. <br />
<br />
===Giulio Tiozzo===<br />
<br />
The notion of contracting element has become central in geometric group theory, <br />
singling out, in an arbitrary metric space, the geodesics which behave like geodesics <br />
in a delta-hyperbolic space. In this work, joint with K. Chawla and I. Choi, we prove <br />
the following characterization of hyperbolic groups: a group is hyperbolic if and only if <br />
the D-contracting elements are generic with respect to counting in the Cayley graph. <br />
<br />
<br />
===Hongming Nie===<br />
<br />
===Luke Jeffreys===<br />
<br />
<br />
===Emily Stark===<br />
<br />
Rigidity problems in geometric group theory frequently have the following form: if two finitely generated groups share a geometric structure, do they share algebraic structure? We consider two finitely generated groups that are either quasi-isometric or act geometrically on the same proper metric space, and we ask if they are virtually isomorphic. The work of Papasoglu--Whyte demonstrates that infinite-ended groups are quasi-isometrically flexible, but our results show that if you assume a common geometric model, then there is often rigidity. To do this, we introduce the notion of a graphically discrete group, which imposes a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds; free groups are non-examples. We will present new examples and demonstrate this property is not a commensurability invariant. We will present rigidity phenomena for free products of graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse.<br />
<br />
<br />
== Spring 2023 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|January 29<br />
|[https://sites.google.com/view/michael-zshornack/home Michael Zshornack] (UCSB)<br />
|TBA<br />
|Zimmer<br />
|}<br />
<br />
|-<br />
|April 29<br />
|[https://sites.google.com/view/chris-leiningers-webpage/home Chris Leininger] (Rice)<br />
|TBA<br />
|Uyanik<br />
|}<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2022-2023 [[Dynamics_Seminar_2022-2023]]<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25244Colloquia2023-09-15T18:18:57Z<p>Amzimmer2: /* Abstracts */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm unless otherwise noted. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
==Fall 2023==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Sept 8<br />
|[https://www.uwlax.edu/profile/tdas/ Tushar Das] (University of Wisconsin-La Crosse)<br />
|Playing games on fractals: Dynamical & Diophantine | Playing games on fractals: Dynamical & Diophantine<br />
|Stovall<br />
|-<br />
|Sept 15<br />
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale)<br />
|Nonlocal PDEs and Quantum Optics<br />
|Li<br />
|-<br />
|Sept 22<br />
|[https://www.dumas.io/ David Dumas](University of Illinois Chicago)<br />
|Geometry of surface group homomorphisms<br />
|Zimmer<br />
|-<br />
|Sept 29<br />
|<br />
|<br />
|<br />
|-<br />
|<b>Monday Oct 2 at 4 pm</b><br />
|[https://www.math.tamu.edu/~titi/ Edriss Titi] (Texas A&M University)<br />
|Distinguished lectures<br />
|Smith, Stechmann<br />
|-<br />
|Oct 13<br />
|Autumn Kent<br />
|The 0π Theorem<br />
|<br />
|-<br />
|Oct 20<br />
|Sara Maloni (UVA)<br />
|<br />
|Dymarz, Uyanik, GmMaW<br />
|-<br />
|<b>Wednesday Oct 25 at 4 pm</b><br />
|[https://math.mit.edu/~gigliola/ Gigliola Staffilani] (MIT)<br />
|<br />
|Ifrim, Smith<br />
|-<br />
|Oct 27<br />
|[https://www.math.purdue.edu/people/bio/banuelos/home Rodrigo Bañuelos] (Purdue)<br />
|<br />
|Stovall<br />
|-<br />
|<b>Tuesday Oct 31 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|Distinguished lectures<br />
|Gurevich<br />
|-<br />
|<b>Wednesday Nov 1 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|Distinguished lectures<br />
|Gurevich<br />
|}<br />
<br />
==Abstracts==<br />
<br />
<br />
<br />
'''Friday, September 8. Tushar Das'''<br />
<br />
Playing games on fractals: Dynamical & Diophantine<br />
We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.<br />
<br />
<br />
'''Friday, September 15. John Schotland'''<br />
<br />
Nonlocal PDEs and Quantum Optics<br />
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.<br />
<br />
'''Friday, September 22. David Dumas'''<br />
<br />
The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics. In this talk I will discuss and weave together two threads of research within this larger story: 1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view"). This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research.<br />
<br />
'''Friday, October 13. Autumn Kent'''<br />
<br />
A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.<br />
<br />
==Future Colloquia==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Spring 2022 Colloquiums|Spring 2022]]<br />
<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=25243Colloquia2023-09-15T18:18:03Z<p>Amzimmer2: /* Fall 2023 */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm unless otherwise noted. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
==Fall 2023==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Sept 8<br />
|[https://www.uwlax.edu/profile/tdas/ Tushar Das] (University of Wisconsin-La Crosse)<br />
|Playing games on fractals: Dynamical & Diophantine | Playing games on fractals: Dynamical & Diophantine<br />
|Stovall<br />
|-<br />
|Sept 15<br />
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale)<br />
|Nonlocal PDEs and Quantum Optics<br />
|Li<br />
|-<br />
|Sept 22<br />
|[https://www.dumas.io/ David Dumas](University of Illinois Chicago)<br />
|Geometry of surface group homomorphisms<br />
|Zimmer<br />
|-<br />
|Sept 29<br />
|<br />
|<br />
|<br />
|-<br />
|<b>Monday Oct 2 at 4 pm</b><br />
|[https://www.math.tamu.edu/~titi/ Edriss Titi] (Texas A&M University)<br />
|Distinguished lectures<br />
|Smith, Stechmann<br />
|-<br />
|Oct 13<br />
|Autumn Kent<br />
|The 0π Theorem<br />
|<br />
|-<br />
|Oct 20<br />
|Sara Maloni (UVA)<br />
|<br />
|Dymarz, Uyanik, GmMaW<br />
|-<br />
|<b>Wednesday Oct 25 at 4 pm</b><br />
|[https://math.mit.edu/~gigliola/ Gigliola Staffilani] (MIT)<br />
|<br />
|Ifrim, Smith<br />
|-<br />
|Oct 27<br />
|[https://www.math.purdue.edu/people/bio/banuelos/home Rodrigo Bañuelos] (Purdue)<br />
|<br />
|Stovall<br />
|-<br />
|<b>Tuesday Oct 31 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|Distinguished lectures<br />
|Gurevich<br />
|-<br />
|<b>Wednesday Nov 1 at 4 pm</b><br />
|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)<br />
|Distinguished lectures<br />
|Gurevich<br />
|}<br />
<br />
==Abstracts==<br />
<br />
<br />
<br />
'''Friday, September 8. Tushar Das'''<br />
<br />
Playing games on fractals: Dynamical & Diophantine<br />
We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.<br />
<br />
<br />
'''Friday, September 15. John Schotland'''<br />
<br />
Nonlocal PDEs and Quantum Optics<br />
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.<br />
<br />
<br />
'''Friday, October 13. Autumn Kent'''<br />
<br />
A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.<br />
<br />
==Future Colloquia==<br />
<br />
[[Colloquia/Spring2024|Spring 2024]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
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[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Spring_2023_Analysis_Seminar&diff=24803Spring 2023 Analysis Seminar2023-04-21T15:35:24Z<p>Amzimmer2: </p>
<hr />
<div>Organizer: Shaoming Guo<br />
<br />
Email: shaomingguo (at) math (dot) wisc (dot) edu<br />
<br />
Time: Tuesdays, 4-5pm<br />
<br />
Room: Van Vleck B139<br />
<br />
All talks will be in-person unless otherwise specified.<br />
<br />
In some cases the seminar may be scheduled at different time to accommodate speakers. <br />
<br />
If you would like to subscribe to the Analysis seminar list, send a blank email to analysis+join (at) g-groups (dot) wisc (dot) edu<br />
{| class="wikitable"<br />
|+<br />
!Date<br />
!Speaker<br />
!Institution<br />
!Title<br />
!Host(s)<br />
|-<br />
|Jan. 24<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|Jan. 31<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|Feb. 7<br />
|Shaoming Guo<br />
|UW Madison<br />
|[[Spring 2023 Analysis Seminar#Shaoming Guo|Hörmander's generalization of the Fourier restriction problem]]<br />
|Analysis group<br />
|-<br />
|Feb. 14<br />
|Diogo Oliveira e Silva<br />
|Instituto Superior Técnico (Lisboa) <br />
|[[Spring 2023 Analysis Seminar#Diogo Olivieira e Silva|The Stein-Tomas inequality: three recent improvements]]<br />
|Betsy Stovall, Andreas Seeger<br />
|-<br />
|Feb. 21<br />
|Jack Burkart<br />
|UW Madison<br />
|[[Spring 2023 Analysis Seminar#Diogo Olivieira e Silva|Sobolev Spaces for General Metric Spaces]]<br />
|Analysis group<br />
|-<br />
|Feb. 28<br />
|Shengwen Gan<br />
|MIT<br />
|[[Spring 2023 Analysis Seminar#Shengwen Gan|Exceptional set estimates in finite field]]<br />
|Analysis group<br />
|-<br />
| Mar. 7<br />
|Yuqiu Fu<br />
|MIT<br />
|[[Spring 2023 Analysis Seminar#Yuqiu Fu|Incidence estimates for tubes and balls with dimensional spacing condition in R^2.]]<br />
|Zane Li<br />
|-<br />
|Mar. 14<br />
|Spring break<br />
|<br />
|<br />
|<br />
|-<br />
|Mar. 21<br />
|Zhiren Wang<br />
|Penn State<br />
|[[Spring 2023 Analysis Seminar#Zhiren Wang|Classification of smooth actions by higher rank lattices in critical dimensions]]<br />
|Shaoming Guo, Chenxi Wu<br />
|-<br />
|Mar. 28<br />
|Jaehyeon Ryu<br />
|KIAS, UW Madison<br />
|[[Spring 2023 Analysis Seminar#Jaehyeon Ryu|Endpoint eigenfunction bounds for the Hermite operator]]<br />
|Analysis group<br />
|-<br />
|Apr. 4<br />
|Liding Yao<br />
|Ohio State<br />
|[[Spring 2023 Analysis Seminar#Jaehyeon Ryu|Sobolev and H\"older Estimates for Homotopy Operators of $\overline\partial$-Equations on Convex Domains of Finite Multitype<br />
]]<br />
||Brian Street<br />
|-<br />
| Apr. 11<br />
| Dominique Maldague<br />
|MIT<br />
|[[Spring 2023 Analysis Seminar#Dominique Maldague|A sharp square function estimate for the moment curve in R^3<br />
]]<br />
|Betsy Stovall, Andreas Seeger<br />
|-<br />
|Apr. 18<br />
|David Beltran<br />
|Universitat de València.<br />
|[[Spring 2023 Analysis Seminar#David Beltran|On sharp isoperimetric inequalities on the hypercube]]<br />
|Andreas Seeger<br />
|-<br />
|Apr. 25<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|May 2<br />
|Lisa Naples<br />
|Macalester College<br />
|<br />
|Jack Burkart<br />
|}<br />
<br />
<br />
=Abstracts=<br />
===[[Shaoming Guo]]===<br />
Title: Hormander's generalization of the Fourier restriction problem<br />
<br />
Abstract: Hörmander 1973 proposed to study a generalized Fourier extension operator, and asked whether the generalized operator satisfies the same L^p bounds as that of the standard Fourier extension operator. Surprisingly, Bourgain 1991 gave a negative answer to Hörmander’s question. In this talk, I will discuss a modification of Hörmander’s question whose answer may be affirmative. This is a joint work with Hong Wang and Ruixiang Zhang.<br />
<br />
<br />
===[[Diogo Oliveira e Silva]]===<br />
Title: The Stein-Tomas inequality: three recent improvements<br />
<br />
Abstract: The Stein-Tomas inequality dates back to 1975 and is a cornerstone of Fourier restriction theory. Despite its respectable age, it is a fertile ground for current research. The goal of this talk is three-fold: we present a recent proof of the sharp endpoint Stein-Tomas inequality in three space dimensions; we present a variational refinement and withdraw some consequences; and we discuss how to improve the Stein-Tomas inequality in the presence of certain symmetries. <br />
<br />
===[[Jack Burkart]]===<br />
Title: Sobolev Spaces for General Metric Spaces<br />
<br />
Abstract: Sobolev spaces are classically defined in Euclidean space as L^p functions possessing weak derivatives (of some order). Recently, there has been interest in doing analysis and developing a theory of calculus on general metric spaces. A natural question one might ask is how can one define Sobolev spaces in an arbitrary metric space? In this talk, I'll discuss some ways we can generalize concepts like the Poincare inequalty to an arbitrary metric space and showcase some alternative definitions that can be used in more general settings. After discussing some known results in this area, I'll spend the latter part of the talk discussing some of my own ongoing research involving establishing Poincare inequalities in domains in Euclidean space that are not necessarily W^{1,p} extension domains and some other questions we are currently considering. This talk features joint and ongoing work with Ryan Alvarado, Lisa Naples, and Benham Esmayli. <br />
<br />
<br />
<br />
===[[Shengwen Gan]]===<br />
Title: Exceptional set estimates in finite field<br />
<br />
Abstract: Let $A\subset \mathbb{F}^3_p$ with $\# A=p^a$. For any direction $\theta$ in $\mathbb{F}^3_p$, define $\pi_{\theta}(A)$ to be the set of lines in direction $\theta$ and passing through $A$. Define the exceptional set $E_s(A):=\{\theta: \# \pi_\theta (A)<p^s \}$. Falconer-type estimate gives $\# E_s(A)\lesssim p^{2+s-a} $. I will talk about a new result: If $s<\frac{a+1}{2}$, then $\# E_s(A)\lesssim p^{2+2s-2a}$. <br />
<br />
<br />
<br />
<br />
===[[Yuqiu Fu]]===<br />
Title: Incidence estimates for tubes and balls with dimensional spacing condition in R^2.<br />
<br />
Abstract: We will discuss essentially sharp incidence estimates in R^2 for a collection of tubes of dimension \delta \times 1 and a collection of balls of radius \delta, which satisfy some dimensional spacing condition. An application of these estimates is a new lower bound on the Hausdorff dimension of a (s,t) – Furstenberg set in R^2 when t > 1 + \epsilon(s,t) and s + t/2 \geq 1, where \epsilon is small depending on (s,t). This is joint work with Kevin Ren.<br />
<br />
<br />
<br />
===[[Zhiren Wang]]===<br />
Title: Classification of smooth actions by higher rank lattices in critical dimensions.<br />
<br />
Abstract: The Zimmer program asks how lattices in higher rank semisimple Lie groups may act smoothly on compact manifolds. Below a certain critical dimension, the recent proof of the Zimmer conjecture by Brown-Fisher-Hurtado asserts that, for SL(n,R) with n\geq 3 or other higher rank R-split semisimple Lie groups, the action is trivial up to a finite group action. In this talk, we will explain what happens in the critical dimension for higher rank R-split semisimple Lie groups. For example, non-trivial actions by lattices in SL(n,R), n\geq 3, on (n-1)-dimensional manifolds are isomorphic to the standard action on RP^{n-1} up to a finite quotient group and a finite covering. This is a joint work with Aaron Brown and Federico Rodriguez Hertz.<br />
<br />
<br />
===[[Jaehyeon Ryu]]===<br />
Title: Endpoint eigenfunction bounds for the Hermite operator<br />
<br />
Abstract: We study the problem of obtaining a sharp $L^2$--$L^q$ bound on the spectral projection operator for the Hermite operator at $q = 2(d+3)/(d+1)$. The point is called the endpoint because in previous related work of Koch-Tataru, the authors obtained sharp $L^2$--$L^q$ bounds except for $q = 2(d+3)/(d+1)$. As for the endpoint, they also obtained a bound involving a logarithmic term, but they did not expect that this bound would be optimal and instead conjectured that the logarithmic term can be removed. In this talk, we prove that this conjecture is true in dimensions greater or equal to 3. This talk is based on a joint work with Eunhee Jeong, Sanghyuk Lee.<br />
<br />
<br />
<br />
===[[Liding Yao]]===<br />
Title: Sobolev and H\"older Estimates for Homotopy Operators of $\overline\partial$-Equations on Convex Domains of Finite Multitype<br />
<br />
Abstract: For a bounded smooth convex domain $\Omega\subset\mathbb C^n$ that has finite type $m$, we construct a $\overline\partial$ solution operator $\mathcal T_q$ on $(0,q)$-forms that has (fractional) Sobolev boundedness $\mathcal T_q:H^{s,p}\to H^{s+1/m,p}$ for all $1<p<\infty$ and $s\in\mathbb R$. In the talk I will briefly repeat the basic materials of $\overline\partial$-Equations (from Spring 2022 Math 921); review the so-called “integral representations” construction; and a new aspect of extension operators on solving $\overline\partial$.<br />
<br />
<br />
<br />
===[[Dominique Maldague]]===<br />
Title: A sharp square function estimate for the moment curve in R^3<br />
<br />
Abstract: I will present recent work which proves a sharp L^7 square function estimate for the moment curve (t , t^2, t^3) in R^3 using ideas from decoupling theory. In the context of restriction theory, in which we consider functions with specialized (curved) Fourier support, this is the only known sharp square function estimate with a non-even L^p exponent (p=7). The basic set-up is to consider a function f with Fourier support in a small neighborhood of the moment curve. Then partition the neighborhood into box-like subsets and form a square function in the Fourier projections of f onto these box-like regions. We will use a combination of recent tools including the "high-low" method and wave envelope estimates to bound f in L^7 by the square function of f in L^7. <br />
<br />
<br />
===[[David Beltran]]===<br />
Title: On sharp isoperimetric inequalities on the hypercube<br />
<br />
Abstract: The classical edge-isoperimetric inequality on the hypercube states that $|\nabla A| \geq |A| \log_2 (1/|A|)$ for any set $A \subseteq \{0,1\}^d$, where $\nabla A$ is the set of edges between A and its complement. This is sharp, since the inequality saturates on any subcube. Extensions and variants of this inequality have been studied by several authors, but so far none of them has the property of saturating on all sucubes. In this talk, we will present such an inequality, as well as improved versions of existing estimates. We will also discuss some applications.<br />
This is joint work with Paata Ivanisvili and José Madrid<br />
<br />
<br />
<br />
<br />
[https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars] Previous Analysis Seminars<br />
<br />
[https://wiki.math.wisc.edu/index.php/Fall_2022_analysis_seminar] Fall 2022 Analysis Seminar</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Whatcha_Doin_Seminar&diff=24334Whatcha Doin Seminar2023-01-31T17:57:34Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>The Whatcha Doin' Seminar is a place where professors can give 20-30 minute talks about their research aimed at beginning graduate students. This will give students an opportunity to meet potential advisors and see what they are up to.<br />
<br />
Time: '''Mondays''' at '''4:30PM'''<br />
<br />
Location: '''Van Vleck B129'''<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |research area<br />
! align="left" |title<br />
|-<br />
|January 30<br />
|Jean-Luc Thiffeault<br />
|Applied Math<br />
|''Active matter''<br />
|-<br />
|February 6<br />
|Dima Arinkin<br />
|Algebraic geometry<br />
|TBA<br />
|-<br />
|February 13<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|February 20<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|February 27<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|March 6<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|March 13<br />
|Spring Break, No Seminar<br />
|<br />
|<br />
|-<br />
|March 20<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|March 27<br />
|Sergey Denisov<br />
|Analysis & PDE<br />
|Title<br />
|-<br />
|April 3<br />
|Andrew Zimmer<br />
|TBA<br />
|TBA<br />
|-<br />
|April 10<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|April 17<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
||April 24<br />
|Speaker<br />
|Subject Area<br />
|Title<br />
|-<br />
|May 1<br />
|Marissa Loving<br />
|Geometry, topology, and dynamics<br />
|TBA<br />
|-<br />
|}</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar_2022-2023&diff=24251Dynamics Seminar 2022-20232023-01-24T15:38:47Z<p>Amzimmer2: /* Spring Abstracts */</p>
<hr />
<div>During the Spring 2023 semester, the [[Dynamics]] seminar meets in room '''2425 of Sterling Hall''' on '''Mondays''' from '''2:30pm - 3:20pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host(s)<br />
|-<br />
|January 30<br />
|[http://websites.umich.edu/~blayac/ Pierre-Louis Blayac] (Michigan)<br />
|[[#Pierre-Louis Blayac| ''Divisible convex sets with properly embedded cones'']]<br />
|Zhu and Zimmer<br />
|-<br />
|February 6<br />
|[http://www-personal.umich.edu/~kbutt/index.html Karen Butt] (Michigan)<br />
|[[#Karen Butt| ''Quantitative marked length spectrum rigidity'']]<br />
|Zimmer<br />
|-<br />
|February 13<br />
|[https://sites.google.com/view/elizabeth-field Elizabeth Field] (Utah)<br />
|[[#Elizabeth Field| ''TBA'']]<br />
|Loving<br />
|-<br />
|February 20<br />
|[https://math.berkeley.edu/~chicheuk/ Chi Cheuk Tsang] (Berkeley)<br />
|[[#Chi Cheuk Tsang| ''Dilatations of pseudo-Anosov maps and standardly embedded train tracks'']]<br />
|Loving<br />
|-<br />
|February 27<br />
|[https://www.caglaruyanik.com/home Caglar Uyanik] (UW Madison)<br />
|[[#Caglar Uyanik| ''TBA'']]<br />
|local<br />
|-<br />
|March 6<br />
|[https://filippomazzoli.github.io Filippo Mazzoli] (UVA)<br />
|[[#Filippo Mazzoli| TBA]]<br />
|Zhu<br />
|-<br />
|March 13<br />
|Spring Break, No Seminar<br />
|<br />
|<br />
|-<br />
|March 20<br />
|[https://www.rosemorriswright.com/ Rose Morris-Wright ] (Middlebury)<br />
|[[#Rose Morris-Wright| ''TBA'']]<br />
|Dymarz<br />
|-<br />
|March 27<br />
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)<br />
|[[#Carolyn Abbott| ''TBA'']]<br />
|Dymarz and Uyanik<br />
|-<br />
|April 3<br />
|[https://sites.google.com/view/sfairchild/home Samantha Fairchild] (Osnabrück)<br />
|TBA<br />
|Apisa<br />
|-<br />
|April 10<br />
|[https://www.math.utah.edu/~chaika/ Jon Chaika] (Utah)<br />
|[[#Jon Chaika| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|April 17<br />
|[https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] (Chicago)<br />
|[[#Mikolaj Fraczyk| ''TBA'']]<br />
|Skenderi and Zimmer<br />
|-<br />
||April 24<br />
|[https://sites.google.com/view/tarikaougab/home/ Tarik Aougab] (Haverford)<br />
|[[#Tarik Aougab| ''TBA'']]<br />
|Loving<br />
|-<br />
|May 1<br />
|[https://www.dmartinezgranado.com Didac Martinez-Granado] (UC Davis)<br />
|[[#Didac Martinez-Granado| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Pierre-Louis Blayac===<br />
<br />
A divisible convex set is a convex, bounded, and open subset of an affine chart of the real projective space, on which acts cocompactly a discrete group of projective transformations. These objects have a very rich theory, which involves ideas from dynamical systems, geometric group theory, (G,X)-structures and Riemannian geometry with nonpositive curvature. Moreover, they are an important source of examples of discrete subgroups of Lie groups; for instance they have links with Anosov representations. In this talk, we will survey known examples of divisible convex sets, and then describe new examples obtained in collaboration with Gabriele Viaggi, of irreducible, non-symmetric, and non-strictly convex divisible convex sets in arbitrary dimensions (at least 3).<br />
<br />
===Karen Butt===<br />
<br />
The marked length spectrum of a closed Riemannian manifold of negative curvature is a function on the free homotopy classes of closed curves which assigns to each class the length of its unique geodesic representative. It is known in certain cases that the marked length spectrum determines the metric up to isometry, and this is conjectured to be true in general. In this talk, we explore to what extent the marked length spectrum on a sufficiently large finite set approximately determines the metric.<br />
<br />
===Elizabeth Field===<br />
<br />
===Chi Cheuk Tsang===<br />
<br />
The dilatation of a pseudo-Anosov map is a measure of the complexity of its dynamics. The minimum dilatation problem asks for the minimum dilatation among all pseudo-Anosov maps defined on a fixed surface, which can be thought of as the smallest amount of mixing one can perform while still doing something topologically interesting. In this talk, we present some recent work on this problem with Eriko Hironaka, which shows a sharp lower bound for dilatations of fully-punctured pseudo-Anosov maps with at least two puncture orbits. We will explain some ideas in the proof, including standardly embedded train tracks and Perron-Frobenius matrices.<br />
<br />
===Caglar Uyanik===<br />
<br />
===Filippo Mazzoli===<br />
<br />
===Rose Morris-Wright===<br />
<br />
===Carolyn Abbott===<br />
<br />
===Samantha Fairchild===<br />
<br />
===Jon Chaika===<br />
<br />
===Mikolaj Fraczyk===<br />
<br />
===Tarik Aougab===<br />
<br />
===Didac Martinez-Granado===<br />
<br />
== Fall 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 12<br />
|[https://math.ou.edu/~jing/ Jing Tao] (OU)<br />
|[[#Jing Tao|Genericity of pseudo-Anosov maps]]<br />
|Dymarz and Uyanik<br />
|-<br />
|September 19<br />
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)(virtual)<br />
|[[#Rebekah Palmer|Totally geodesic surfaces in knot complements]]<br />
|VIRTUAL<br />
|-<br />
|September 26<br />
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)<br />
|[[#Beibei Liu|The critical exponent: old and new]]<br />
| Dymarz<br />
|-<br />
|October 3<br />
|Grace Work (UW-Madison)<br />
|[[#Grace Work |Discretely shrinking targets in moduli space]]<br />
|local<br />
|-<br />
|October 10<br />
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)<br />
|[[#Jean Pierre Mutanguha| Canonical forms for free group automorphisms]]<br />
|Uyanik<br />
|-<br />
|October 17<br />
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)<br />
|[[#Anthony Sanchez | Kontsevich-Zorich monodromy groups of translation covers of some platonic solids]]<br />
|Uyanik<br />
|-<br />
|October 24<br />
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (U Chicago)<br />
|postponed<br />
|Uyanik and Work<br />
|-<br />
|October 31<br />
|[https://sites.google.com/view/zhufeng-math/home Feng Zhu] (UW Madison)<br />
|[[#Feng Zhu| ''Relatively Anosov representations: a dynamical notion of geometric finiteness'']]<br />
|local<br />
|-<br />
|November 7<br />
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)<br />
|[[#Ethan Farber| ''Pseudo-Anosovs of interval type'']]<br />
|Loving<br />
|-<br />
|November 14<br />
|[https://www.math.montana.edu/geyer/ Lukas Geyer] (Montana) <br />
|[[#Lukas Geyer| ''Classification of critically fixed anti-Thurston maps'']]<br />
|Burkart<br />
|-<br />
|November 21<br />
|[http://www.hbaik.org/ Harry Hyungryul Baik] (KAIST)<br />
|[[#Harry Baik| ''Revisit the theory of laminar groups'']]<br />
|Wu<br />
|-<br />
|November 28<br />
|[https://mmontee.people.sites.carleton.edu MurphyKate Montee] (Carleton)<br />
|[[#MurphyKate Montee | ''Cubulation and Property (T) in random groups'']]<br />
|Dymarz<br />
|-<br />
|December 5<br />
|[https://sites.google.com/view/lovingmath/home Marissa Loving] (UW Madison)<br />
|[[#Marissa Loving|Unmarked simple length spectral rigidity for covers]]<br />
|local<br />
|-<br />
|December 12<br />
|[https://scholar.harvard.edu/tinatorkaman/home Tina Torkaman] (Harvard)<br />
|[[#Tina Torkaman| '' Intersection number and intersection points of closed geodesics on hyperbolic surfaces'']]<br />
|Uyanik<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Jing Tao===<br />
By Nielsen-Thurston classification, every homeomorphism of a surface is isotopic to one of three types: finite order, reducible, or pseudo-Anosov. While there are these three types, it is natural to wonder which type is more prevalent. In any reasonable way to sample matrices in SL(2,Z), irreducible matrices should be generic. One expects something similar for pseudo-Anosov maps. In joint work with Erlandsson and Souto, we define a notion of genericity and show that pseudo-Anosov maps are indeed generic. More precisely, we consider several "norms" on the mapping class group of the surface, and show that the proportion of pseudo-Anosov maps in a ball of radius r tends to 1 as r tends to infinity. The norms can be thought of as the natural analogues of matrix norms on SL(2,Z).<br />
<br />
===Rebekah Palmer===<br />
Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader--Fisher--Miller--Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case. In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces. On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover. This talk will explore this progress for both the uniqueness and the absence.<br />
<br />
===Beibei Liu===<br />
The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higher-rank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the Patterson-Sullivan theory and introduce new results about Kleinian groups with small or large critical exponents. <br />
<br />
===Grace Work===<br />
The shrinking target problem characterizes when there is a full measure set of points that hit a decreasing family of target sets under a given flow. This question is closely related to the Borel Cantilli lemma and also gives rise to logarithm laws. We will examine the discrete shrinking target problem in a general and then more specifically in the setting of Teichmuller flow on the moduli space of unit-area quadratic differentials.<br />
<br />
===Jean Pierre Mutanguha===<br />
The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!<br />
<br />
===Anthony Sanchez===<br />
Platonic solids have been studied for thousands of years. By unfolding a platonic solid we can associate to it a translation surface. Interesting information about the underlying platonic solid can be discovered in the cover where more (dynamical and geometric) structure is present. The translation covers we consider have a large group of symmetries that leave the global composition of the surface unchanged. However, the local structure of paths on the surface is often sensitive to these symmetries. The Kontsevich-Zorich mondromy group keeps track of this sensitivity. <br />
<br />
In joint work with R. Gutiérrez-Romo and D. Lee, we study the monodromy groups of translation covers of some platonic solids and show that the Zariski closure is a power of SL(2,R). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound").<br />
<br />
===Feng Zhu===<br />
<br />
Putting hyperbolic metrics on a finite-type surface S gives us linear representations of the fundamental group of S into PSL(2,R) with many nice geometric and dynamical properties: for instance they are discrete and faithful, and in fact stably quasi-isometrically embedded.<br />
<br />
In this talk, we will introduce (relatively) Anosov representations, which generalise this picture to higher-rank Lie groups such as PSL(d,R) for d>2, giving us a class of (relatively) hyperbolic subgroups there with similarly good geometric and dynamical properties.<br />
<br />
This is mostly joint work with Andrew Zimmer.<br />
<br />
===Ethan Farber===<br />
<br />
A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional topologists and dynamicists for the past forty years. We show that any pA on the sphere whose associated quadratic differential has at most one zero, admits an invariant train track whose expanding subgraph is an interval. Concretely, such a pA has the dynamics of an interval map. As an application, we recover a uniform lower bound on the entropy of these pAs originally due to Boissy-Lanneau. Time permitting, we will also discuss potential applications to a question of Fried. This is joint work with Karl Winsor.<br />
<br />
===Lukas Geyer===<br />
<br />
Recently there has been an increased interest in complex dynamics of orientation-reversing maps, in particular in the context of gravitational lensing and as an analogue of reflection groups in Sullivan's dictionary between Kleinian groups and dynamics of (anti-)rational maps. Much of the theory parallels the orientation-preserving case, but there are some intriguing differences. In order to deal with the post-critically finite case, we study anti-Thurston maps (orientation-reversing versions of Thurston maps), and prove an orientation-reversing analogue of Thurston's topological classification of post-critically finite rational maps, as well as the canonical decomposition of obstructed maps, following Pilgrim and Selinger. Using these tools, we obtain a combinatorial classification of critically fixed anti-Thurston maps, extending a recently obtained classification of critically fixed anti-rational maps. If time allows, I will explain applications of this classification to gravitational lensing. Most of this is based on joint work with Mikhail Hlushchanka.<br />
<br />
===Harry Baik ===<br />
<br />
I will give a brief introduction to laminar groups which are groups of orientation-preserving homeomorphisms of the circle admitting invariant laminations. The term was coined by Calegari and the study of laminar groups was motivated by work of Thurston and Calegari-Dunfield. We present old and new results on laminar groups which tell us when a given laminar group is either fuchsian or Kleinian. This is based on joint work with KyeongRo Kim and Hongtaek Jung.<br />
<br />
===MurphyKate Montee===<br />
<br />
Random groups are one way to study "typical" behavior of groups. In the Gromov density model, we often find that properties have a threshold density above which the property is satisfied with probability 1, and below which it is satisfied with probability 0. Two properties of random groups that have been well studied are cubulation (and relaxations of this property) and Property (T). In this setting these are mutually exclusive properties, but threshold densities are not known for either property. In this talk I'll present the current state of the art regarding these properties in random groups, and discuss some ways to further these results.<br />
<br />
===Marissa Loving===<br />
A fundamental question in geometry is the extent to which a manifold M is determined by its length spectrum, i.e. the collection of lengths of closed geodesics on M. This has been studied extensively for flat, hyperbolic, and negatively curved metrics. In this talk, we will focus on surfaces equipped with a choice of hyperbolic metric. We will explore the space between (1) work of Otal (resp. Fricke) which asserts that the marked length spectrum (resp. marked ''simple'' length spectrum) determines a hyperbolic surface, and (2) celebrated constructions of Vignéras and Sunada, which show that this rigidity fails when we forget the marking. In particular, we will consider the extent to which the unmarked simple length spectrum distinguishes between hyperbolic surfaces arising from Sunada’s construction. This represents joint work with Tarik Aougab, Max Lahn, and Nick Miller.<br />
<br />
===Tina Torkaman===<br />
<br />
In this talk, I will talk about the (geometric) intersection number between closed geodesics on finite volume hyperbolic surfaces. Specifically, I will discuss the optimum upper bound on the intersection number in terms of the product of hyperbolic lengths. I also talk about the equidistribution of the intersection points between closed geodesics.<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar_2022-2023&diff=24250Dynamics Seminar 2022-20232023-01-24T15:37:20Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>During the Spring 2023 semester, the [[Dynamics]] seminar meets in room '''2425 of Sterling Hall''' on '''Mondays''' from '''2:30pm - 3:20pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host(s)<br />
|-<br />
|January 30<br />
|[http://websites.umich.edu/~blayac/ Pierre-Louis Blayac] (Michigan)<br />
|[[#Pierre-Louis Blayac| ''Divisible convex sets with properly embedded cones'']]<br />
|Zhu and Zimmer<br />
|-<br />
|February 6<br />
|[http://www-personal.umich.edu/~kbutt/index.html Karen Butt] (Michigan)<br />
|[[#Karen Butt| ''Quantitative marked length spectrum rigidity'']]<br />
|Zimmer<br />
|-<br />
|February 13<br />
|[https://sites.google.com/view/elizabeth-field Elizabeth Field] (Utah)<br />
|[[#Elizabeth Field| ''TBA'']]<br />
|Loving<br />
|-<br />
|February 20<br />
|[https://math.berkeley.edu/~chicheuk/ Chi Cheuk Tsang] (Berkeley)<br />
|[[#Chi Cheuk Tsang| ''Dilatations of pseudo-Anosov maps and standardly embedded train tracks'']]<br />
|Loving<br />
|-<br />
|February 27<br />
|[https://www.caglaruyanik.com/home Caglar Uyanik] (UW Madison)<br />
|[[#Caglar Uyanik| ''TBA'']]<br />
|local<br />
|-<br />
|March 6<br />
|[https://filippomazzoli.github.io Filippo Mazzoli] (UVA)<br />
|[[#Filippo Mazzoli| TBA]]<br />
|Zhu<br />
|-<br />
|March 13<br />
|Spring Break, No Seminar<br />
|<br />
|<br />
|-<br />
|March 20<br />
|[https://www.rosemorriswright.com/ Rose Morris-Wright ] (Middlebury)<br />
|[[#Rose Morris-Wright| ''TBA'']]<br />
|Dymarz<br />
|-<br />
|March 27<br />
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)<br />
|[[#Carolyn Abbott| ''TBA'']]<br />
|Dymarz and Uyanik<br />
|-<br />
|April 3<br />
|[https://sites.google.com/view/sfairchild/home Samantha Fairchild] (Osnabrück)<br />
|TBA<br />
|Apisa<br />
|-<br />
|April 10<br />
|[https://www.math.utah.edu/~chaika/ Jon Chaika] (Utah)<br />
|[[#Jon Chaika| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|April 17<br />
|[https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] (Chicago)<br />
|[[#Mikolaj Fraczyk| ''TBA'']]<br />
|Skenderi and Zimmer<br />
|-<br />
||April 24<br />
|[https://sites.google.com/view/tarikaougab/home/ Tarik Aougab] (Haverford)<br />
|[[#Tarik Aougab| ''TBA'']]<br />
|Loving<br />
|-<br />
|May 1<br />
|[https://www.dmartinezgranado.com Didac Martinez-Granado] (UC Davis)<br />
|[[#Didac Martinez-Granado| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Pierre-Louis Blayac===<br />
<br />
===Karen Butt===<br />
The marked length spectrum of a closed Riemannian manifold of negative curvature is a function on the free homotopy classes of closed curves which assigns to each class the length of its unique geodesic representative. It is known in certain cases that the marked length spectrum determines the metric up to isometry, and this is conjectured to be true in general. In this talk, we explore to what extent the marked length spectrum on a sufficiently large finite set approximately determines the metric.<br />
<br />
===Elizabeth Field===<br />
<br />
===Chi Cheuk Tsang===<br />
<br />
The dilatation of a pseudo-Anosov map is a measure of the complexity of its dynamics. The minimum dilatation problem asks for the minimum dilatation among all pseudo-Anosov maps defined on a fixed surface, which can be thought of as the smallest amount of mixing one can perform while still doing something topologically interesting. In this talk, we present some recent work on this problem with Eriko Hironaka, which shows a sharp lower bound for dilatations of fully-punctured pseudo-Anosov maps with at least two puncture orbits. We will explain some ideas in the proof, including standardly embedded train tracks and Perron-Frobenius matrices.<br />
<br />
===Caglar Uyanik===<br />
<br />
===Filippo Mazzoli===<br />
<br />
===Rose Morris-Wright===<br />
<br />
===Carolyn Abbott===<br />
<br />
===Samantha Fairchild===<br />
<br />
===Jon Chaika===<br />
<br />
===Mikolaj Fraczyk===<br />
<br />
===Tarik Aougab===<br />
<br />
===Didac Martinez-Granado===<br />
<br />
<br />
== Fall 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 12<br />
|[https://math.ou.edu/~jing/ Jing Tao] (OU)<br />
|[[#Jing Tao|Genericity of pseudo-Anosov maps]]<br />
|Dymarz and Uyanik<br />
|-<br />
|September 19<br />
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)(virtual)<br />
|[[#Rebekah Palmer|Totally geodesic surfaces in knot complements]]<br />
|VIRTUAL<br />
|-<br />
|September 26<br />
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)<br />
|[[#Beibei Liu|The critical exponent: old and new]]<br />
| Dymarz<br />
|-<br />
|October 3<br />
|Grace Work (UW-Madison)<br />
|[[#Grace Work |Discretely shrinking targets in moduli space]]<br />
|local<br />
|-<br />
|October 10<br />
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)<br />
|[[#Jean Pierre Mutanguha| Canonical forms for free group automorphisms]]<br />
|Uyanik<br />
|-<br />
|October 17<br />
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)<br />
|[[#Anthony Sanchez | Kontsevich-Zorich monodromy groups of translation covers of some platonic solids]]<br />
|Uyanik<br />
|-<br />
|October 24<br />
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (U Chicago)<br />
|postponed<br />
|Uyanik and Work<br />
|-<br />
|October 31<br />
|[https://sites.google.com/view/zhufeng-math/home Feng Zhu] (UW Madison)<br />
|[[#Feng Zhu| ''Relatively Anosov representations: a dynamical notion of geometric finiteness'']]<br />
|local<br />
|-<br />
|November 7<br />
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)<br />
|[[#Ethan Farber| ''Pseudo-Anosovs of interval type'']]<br />
|Loving<br />
|-<br />
|November 14<br />
|[https://www.math.montana.edu/geyer/ Lukas Geyer] (Montana) <br />
|[[#Lukas Geyer| ''Classification of critically fixed anti-Thurston maps'']]<br />
|Burkart<br />
|-<br />
|November 21<br />
|[http://www.hbaik.org/ Harry Hyungryul Baik] (KAIST)<br />
|[[#Harry Baik| ''Revisit the theory of laminar groups'']]<br />
|Wu<br />
|-<br />
|November 28<br />
|[https://mmontee.people.sites.carleton.edu MurphyKate Montee] (Carleton)<br />
|[[#MurphyKate Montee | ''Cubulation and Property (T) in random groups'']]<br />
|Dymarz<br />
|-<br />
|December 5<br />
|[https://sites.google.com/view/lovingmath/home Marissa Loving] (UW Madison)<br />
|[[#Marissa Loving|Unmarked simple length spectral rigidity for covers]]<br />
|local<br />
|-<br />
|December 12<br />
|[https://scholar.harvard.edu/tinatorkaman/home Tina Torkaman] (Harvard)<br />
|[[#Tina Torkaman| '' Intersection number and intersection points of closed geodesics on hyperbolic surfaces'']]<br />
|Uyanik<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Jing Tao===<br />
By Nielsen-Thurston classification, every homeomorphism of a surface is isotopic to one of three types: finite order, reducible, or pseudo-Anosov. While there are these three types, it is natural to wonder which type is more prevalent. In any reasonable way to sample matrices in SL(2,Z), irreducible matrices should be generic. One expects something similar for pseudo-Anosov maps. In joint work with Erlandsson and Souto, we define a notion of genericity and show that pseudo-Anosov maps are indeed generic. More precisely, we consider several "norms" on the mapping class group of the surface, and show that the proportion of pseudo-Anosov maps in a ball of radius r tends to 1 as r tends to infinity. The norms can be thought of as the natural analogues of matrix norms on SL(2,Z).<br />
<br />
===Rebekah Palmer===<br />
Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader--Fisher--Miller--Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case. In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces. On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover. This talk will explore this progress for both the uniqueness and the absence.<br />
<br />
===Beibei Liu===<br />
The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higher-rank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the Patterson-Sullivan theory and introduce new results about Kleinian groups with small or large critical exponents. <br />
<br />
===Grace Work===<br />
The shrinking target problem characterizes when there is a full measure set of points that hit a decreasing family of target sets under a given flow. This question is closely related to the Borel Cantilli lemma and also gives rise to logarithm laws. We will examine the discrete shrinking target problem in a general and then more specifically in the setting of Teichmuller flow on the moduli space of unit-area quadratic differentials.<br />
<br />
===Jean Pierre Mutanguha===<br />
The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!<br />
<br />
===Anthony Sanchez===<br />
Platonic solids have been studied for thousands of years. By unfolding a platonic solid we can associate to it a translation surface. Interesting information about the underlying platonic solid can be discovered in the cover where more (dynamical and geometric) structure is present. The translation covers we consider have a large group of symmetries that leave the global composition of the surface unchanged. However, the local structure of paths on the surface is often sensitive to these symmetries. The Kontsevich-Zorich mondromy group keeps track of this sensitivity. <br />
<br />
In joint work with R. Gutiérrez-Romo and D. Lee, we study the monodromy groups of translation covers of some platonic solids and show that the Zariski closure is a power of SL(2,R). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound").<br />
<br />
===Feng Zhu===<br />
<br />
Putting hyperbolic metrics on a finite-type surface S gives us linear representations of the fundamental group of S into PSL(2,R) with many nice geometric and dynamical properties: for instance they are discrete and faithful, and in fact stably quasi-isometrically embedded.<br />
<br />
In this talk, we will introduce (relatively) Anosov representations, which generalise this picture to higher-rank Lie groups such as PSL(d,R) for d>2, giving us a class of (relatively) hyperbolic subgroups there with similarly good geometric and dynamical properties.<br />
<br />
This is mostly joint work with Andrew Zimmer.<br />
<br />
===Ethan Farber===<br />
<br />
A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional topologists and dynamicists for the past forty years. We show that any pA on the sphere whose associated quadratic differential has at most one zero, admits an invariant train track whose expanding subgraph is an interval. Concretely, such a pA has the dynamics of an interval map. As an application, we recover a uniform lower bound on the entropy of these pAs originally due to Boissy-Lanneau. Time permitting, we will also discuss potential applications to a question of Fried. This is joint work with Karl Winsor.<br />
<br />
===Lukas Geyer===<br />
<br />
Recently there has been an increased interest in complex dynamics of orientation-reversing maps, in particular in the context of gravitational lensing and as an analogue of reflection groups in Sullivan's dictionary between Kleinian groups and dynamics of (anti-)rational maps. Much of the theory parallels the orientation-preserving case, but there are some intriguing differences. In order to deal with the post-critically finite case, we study anti-Thurston maps (orientation-reversing versions of Thurston maps), and prove an orientation-reversing analogue of Thurston's topological classification of post-critically finite rational maps, as well as the canonical decomposition of obstructed maps, following Pilgrim and Selinger. Using these tools, we obtain a combinatorial classification of critically fixed anti-Thurston maps, extending a recently obtained classification of critically fixed anti-rational maps. If time allows, I will explain applications of this classification to gravitational lensing. Most of this is based on joint work with Mikhail Hlushchanka.<br />
<br />
===Harry Baik ===<br />
<br />
I will give a brief introduction to laminar groups which are groups of orientation-preserving homeomorphisms of the circle admitting invariant laminations. The term was coined by Calegari and the study of laminar groups was motivated by work of Thurston and Calegari-Dunfield. We present old and new results on laminar groups which tell us when a given laminar group is either fuchsian or Kleinian. This is based on joint work with KyeongRo Kim and Hongtaek Jung.<br />
<br />
===MurphyKate Montee===<br />
<br />
Random groups are one way to study "typical" behavior of groups. In the Gromov density model, we often find that properties have a threshold density above which the property is satisfied with probability 1, and below which it is satisfied with probability 0. Two properties of random groups that have been well studied are cubulation (and relaxations of this property) and Property (T). In this setting these are mutually exclusive properties, but threshold densities are not known for either property. In this talk I'll present the current state of the art regarding these properties in random groups, and discuss some ways to further these results.<br />
<br />
===Marissa Loving===<br />
A fundamental question in geometry is the extent to which a manifold M is determined by its length spectrum, i.e. the collection of lengths of closed geodesics on M. This has been studied extensively for flat, hyperbolic, and negatively curved metrics. In this talk, we will focus on surfaces equipped with a choice of hyperbolic metric. We will explore the space between (1) work of Otal (resp. Fricke) which asserts that the marked length spectrum (resp. marked ''simple'' length spectrum) determines a hyperbolic surface, and (2) celebrated constructions of Vignéras and Sunada, which show that this rigidity fails when we forget the marking. In particular, we will consider the extent to which the unmarked simple length spectrum distinguishes between hyperbolic surfaces arising from Sunada’s construction. This represents joint work with Tarik Aougab, Max Lahn, and Nick Miller.<br />
<br />
===Tina Torkaman===<br />
<br />
In this talk, I will talk about the (geometric) intersection number between closed geodesics on finite volume hyperbolic surfaces. Specifically, I will discuss the optimum upper bound on the intersection number in terms of the product of hyperbolic lengths. I also talk about the equidistribution of the intersection points between closed geodesics.<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar_2022-2023&diff=24232Dynamics Seminar 2022-20232023-01-22T21:02:49Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>During the Spring 2023 semester, the [[Dynamics]] seminar meets in room '''2425 of Sterling Hall''' on '''Mondays''' from '''2:30pm - 3:20pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host(s)<br />
|-<br />
|January 30<br />
|[http://websites.umich.edu/~blayac/ Pierre-Louis Blayac] (Michigan)<br />
|[[#Pierre-Louis Blayac| ''TBA'']]<br />
|Zhu and Zimmer<br />
|-<br />
|February 6<br />
|[http://www-personal.umich.edu/~kbutt/index.html Karen Butt] (Michigan)<br />
|[[#Karen Butt| ''Quantitative marked length spectrum rigidity'']]<br />
|Zimmer<br />
|-<br />
|February 13<br />
|[https://sites.google.com/view/elizabeth-field Elizabeth Field] (Utah)<br />
|[[#Elizabeth Field| ''TBA'']]<br />
|Loving<br />
|-<br />
|February 20<br />
|[https://math.berkeley.edu/~chicheuk/ Chi Cheuk Tsang] (Berkeley)<br />
|[[#Chi Cheuk Tsang| ''Dilatations of pseudo-Anosov maps and standardly embedded train tracks'']]<br />
|Loving<br />
|-<br />
|February 27<br />
|[https://www.caglaruyanik.com/home Caglar Uyanik] (UW Madison)<br />
|[[#Caglar Uyanik| ''TBA'']]<br />
|local<br />
|-<br />
|March 6<br />
|[https://filippomazzoli.github.io Filippo Mazzoli] (UVA)<br />
|[[#Filippo Mazzoli| TBA]]<br />
|Zhu<br />
|-<br />
|March 13<br />
|Spring Break, No Seminar<br />
|<br />
|<br />
|-<br />
|March 20<br />
|[https://www.rosemorriswright.com/ Rose Morris-Wright ] (Middlebury)<br />
|[[#Rose Morris-Wright| ''TBA'']]<br />
|Dymarz<br />
|-<br />
|March 27<br />
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)<br />
|[[#Carolyn Abbott| ''TBA'']]<br />
|Dymarz and Uyanik<br />
|-<br />
|April 3<br />
|[https://sites.google.com/view/sfairchild/home Samantha Fairchild] (Osnabrück)<br />
|TBA<br />
|Apisa<br />
|-<br />
|April 10<br />
|[https://www.math.utah.edu/~chaika/ Jon Chaika] (Utah)<br />
|[[#Jon Chaika| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|April 17<br />
|[https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] (Chicago)<br />
|[[#Mikolaj Fraczyk| ''TBA'']]<br />
|Skenderi and Zimmer<br />
|-<br />
||April 24<br />
|[https://sites.google.com/view/tarikaougab/home/ Tarik Aougab] (Haverford)<br />
|[[#Tarik Aougab| ''TBA'']]<br />
|Loving<br />
|-<br />
|May 1<br />
|[https://www.dmartinezgranado.com Didac Martinez-Granado] (UC Davis)<br />
|[[#Didac Martinez-Granado| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Pierre-Louis Blayac===<br />
<br />
===Karen Butt===<br />
The marked length spectrum of a closed Riemannian manifold of negative curvature is a function on the free homotopy classes of closed curves which assigns to each class the length of its unique geodesic representative. It is known in certain cases that the marked length spectrum determines the metric up to isometry, and this is conjectured to be true in general. In this talk, we explore to what extent the marked length spectrum on a sufficiently large finite set approximately determines the metric.<br />
<br />
===Elizabeth Field===<br />
<br />
===Chi Cheuk Tsang===<br />
<br />
The dilatation of a pseudo-Anosov map is a measure of the complexity of its dynamics. The minimum dilatation problem asks for the minimum dilatation among all pseudo-Anosov maps defined on a fixed surface, which can be thought of as the smallest amount of mixing one can perform while still doing something topologically interesting. In this talk, we present some recent work on this problem with Eriko Hironaka, which shows a sharp lower bound for dilatations of fully-punctured pseudo-Anosov maps with at least two puncture orbits. We will explain some ideas in the proof, including standardly embedded train tracks and Perron-Frobenius matrices.<br />
<br />
===Caglar Uyanik===<br />
<br />
===Filippo Mazzoli===<br />
<br />
===Rose Morris-Wright===<br />
<br />
===Carolyn Abbott===<br />
<br />
===Samantha Fairchild===<br />
<br />
===Jon Chaika===<br />
<br />
===Mikolaj Fraczyk===<br />
<br />
===Tarik Aougab===<br />
<br />
===Didac Martinez-Granado===<br />
<br />
<br />
== Fall 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 12<br />
|[https://math.ou.edu/~jing/ Jing Tao] (OU)<br />
|[[#Jing Tao|Genericity of pseudo-Anosov maps]]<br />
|Dymarz and Uyanik<br />
|-<br />
|September 19<br />
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)(virtual)<br />
|[[#Rebekah Palmer|Totally geodesic surfaces in knot complements]]<br />
|VIRTUAL<br />
|-<br />
|September 26<br />
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)<br />
|[[#Beibei Liu|The critical exponent: old and new]]<br />
| Dymarz<br />
|-<br />
|October 3<br />
|Grace Work (UW-Madison)<br />
|[[#Grace Work |Discretely shrinking targets in moduli space]]<br />
|local<br />
|-<br />
|October 10<br />
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)<br />
|[[#Jean Pierre Mutanguha| Canonical forms for free group automorphisms]]<br />
|Uyanik<br />
|-<br />
|October 17<br />
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)<br />
|[[#Anthony Sanchez | Kontsevich-Zorich monodromy groups of translation covers of some platonic solids]]<br />
|Uyanik<br />
|-<br />
|October 24<br />
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (U Chicago)<br />
|postponed<br />
|Uyanik and Work<br />
|-<br />
|October 31<br />
|[https://sites.google.com/view/zhufeng-math/home Feng Zhu] (UW Madison)<br />
|[[#Feng Zhu| ''Relatively Anosov representations: a dynamical notion of geometric finiteness'']]<br />
|local<br />
|-<br />
|November 7<br />
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)<br />
|[[#Ethan Farber| ''Pseudo-Anosovs of interval type'']]<br />
|Loving<br />
|-<br />
|November 14<br />
|[https://www.math.montana.edu/geyer/ Lukas Geyer] (Montana) <br />
|[[#Lukas Geyer| ''Classification of critically fixed anti-Thurston maps'']]<br />
|Burkart<br />
|-<br />
|November 21<br />
|[http://www.hbaik.org/ Harry Hyungryul Baik] (KAIST)<br />
|[[#Harry Baik| ''Revisit the theory of laminar groups'']]<br />
|Wu<br />
|-<br />
|November 28<br />
|[https://mmontee.people.sites.carleton.edu MurphyKate Montee] (Carleton)<br />
|[[#MurphyKate Montee | ''Cubulation and Property (T) in random groups'']]<br />
|Dymarz<br />
|-<br />
|December 5<br />
|[https://sites.google.com/view/lovingmath/home Marissa Loving] (UW Madison)<br />
|[[#Marissa Loving|Unmarked simple length spectral rigidity for covers]]<br />
|local<br />
|-<br />
|December 12<br />
|[https://scholar.harvard.edu/tinatorkaman/home Tina Torkaman] (Harvard)<br />
|[[#Tina Torkaman| '' Intersection number and intersection points of closed geodesics on hyperbolic surfaces'']]<br />
|Uyanik<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Jing Tao===<br />
By Nielsen-Thurston classification, every homeomorphism of a surface is isotopic to one of three types: finite order, reducible, or pseudo-Anosov. While there are these three types, it is natural to wonder which type is more prevalent. In any reasonable way to sample matrices in SL(2,Z), irreducible matrices should be generic. One expects something similar for pseudo-Anosov maps. In joint work with Erlandsson and Souto, we define a notion of genericity and show that pseudo-Anosov maps are indeed generic. More precisely, we consider several "norms" on the mapping class group of the surface, and show that the proportion of pseudo-Anosov maps in a ball of radius r tends to 1 as r tends to infinity. The norms can be thought of as the natural analogues of matrix norms on SL(2,Z).<br />
<br />
===Rebekah Palmer===<br />
Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader--Fisher--Miller--Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case. In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces. On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover. This talk will explore this progress for both the uniqueness and the absence.<br />
<br />
===Beibei Liu===<br />
The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higher-rank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the Patterson-Sullivan theory and introduce new results about Kleinian groups with small or large critical exponents. <br />
<br />
===Grace Work===<br />
The shrinking target problem characterizes when there is a full measure set of points that hit a decreasing family of target sets under a given flow. This question is closely related to the Borel Cantilli lemma and also gives rise to logarithm laws. We will examine the discrete shrinking target problem in a general and then more specifically in the setting of Teichmuller flow on the moduli space of unit-area quadratic differentials.<br />
<br />
===Jean Pierre Mutanguha===<br />
The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!<br />
<br />
===Anthony Sanchez===<br />
Platonic solids have been studied for thousands of years. By unfolding a platonic solid we can associate to it a translation surface. Interesting information about the underlying platonic solid can be discovered in the cover where more (dynamical and geometric) structure is present. The translation covers we consider have a large group of symmetries that leave the global composition of the surface unchanged. However, the local structure of paths on the surface is often sensitive to these symmetries. The Kontsevich-Zorich mondromy group keeps track of this sensitivity. <br />
<br />
In joint work with R. Gutiérrez-Romo and D. Lee, we study the monodromy groups of translation covers of some platonic solids and show that the Zariski closure is a power of SL(2,R). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound").<br />
<br />
===Feng Zhu===<br />
<br />
Putting hyperbolic metrics on a finite-type surface S gives us linear representations of the fundamental group of S into PSL(2,R) with many nice geometric and dynamical properties: for instance they are discrete and faithful, and in fact stably quasi-isometrically embedded.<br />
<br />
In this talk, we will introduce (relatively) Anosov representations, which generalise this picture to higher-rank Lie groups such as PSL(d,R) for d>2, giving us a class of (relatively) hyperbolic subgroups there with similarly good geometric and dynamical properties.<br />
<br />
This is mostly joint work with Andrew Zimmer.<br />
<br />
===Ethan Farber===<br />
<br />
A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional topologists and dynamicists for the past forty years. We show that any pA on the sphere whose associated quadratic differential has at most one zero, admits an invariant train track whose expanding subgraph is an interval. Concretely, such a pA has the dynamics of an interval map. As an application, we recover a uniform lower bound on the entropy of these pAs originally due to Boissy-Lanneau. Time permitting, we will also discuss potential applications to a question of Fried. This is joint work with Karl Winsor.<br />
<br />
===Lukas Geyer===<br />
<br />
Recently there has been an increased interest in complex dynamics of orientation-reversing maps, in particular in the context of gravitational lensing and as an analogue of reflection groups in Sullivan's dictionary between Kleinian groups and dynamics of (anti-)rational maps. Much of the theory parallels the orientation-preserving case, but there are some intriguing differences. In order to deal with the post-critically finite case, we study anti-Thurston maps (orientation-reversing versions of Thurston maps), and prove an orientation-reversing analogue of Thurston's topological classification of post-critically finite rational maps, as well as the canonical decomposition of obstructed maps, following Pilgrim and Selinger. Using these tools, we obtain a combinatorial classification of critically fixed anti-Thurston maps, extending a recently obtained classification of critically fixed anti-rational maps. If time allows, I will explain applications of this classification to gravitational lensing. Most of this is based on joint work with Mikhail Hlushchanka.<br />
<br />
===Harry Baik ===<br />
<br />
I will give a brief introduction to laminar groups which are groups of orientation-preserving homeomorphisms of the circle admitting invariant laminations. The term was coined by Calegari and the study of laminar groups was motivated by work of Thurston and Calegari-Dunfield. We present old and new results on laminar groups which tell us when a given laminar group is either fuchsian or Kleinian. This is based on joint work with KyeongRo Kim and Hongtaek Jung.<br />
<br />
===MurphyKate Montee===<br />
<br />
Random groups are one way to study "typical" behavior of groups. In the Gromov density model, we often find that properties have a threshold density above which the property is satisfied with probability 1, and below which it is satisfied with probability 0. Two properties of random groups that have been well studied are cubulation (and relaxations of this property) and Property (T). In this setting these are mutually exclusive properties, but threshold densities are not known for either property. In this talk I'll present the current state of the art regarding these properties in random groups, and discuss some ways to further these results.<br />
<br />
===Marissa Loving===<br />
A fundamental question in geometry is the extent to which a manifold M is determined by its length spectrum, i.e. the collection of lengths of closed geodesics on M. This has been studied extensively for flat, hyperbolic, and negatively curved metrics. In this talk, we will focus on surfaces equipped with a choice of hyperbolic metric. We will explore the space between (1) work of Otal (resp. Fricke) which asserts that the marked length spectrum (resp. marked ''simple'' length spectrum) determines a hyperbolic surface, and (2) celebrated constructions of Vignéras and Sunada, which show that this rigidity fails when we forget the marking. In particular, we will consider the extent to which the unmarked simple length spectrum distinguishes between hyperbolic surfaces arising from Sunada’s construction. This represents joint work with Tarik Aougab, Max Lahn, and Nick Miller.<br />
<br />
===Tina Torkaman===<br />
<br />
In this talk, I will talk about the (geometric) intersection number between closed geodesics on finite volume hyperbolic surfaces. Specifically, I will discuss the optimum upper bound on the intersection number in terms of the product of hyperbolic lengths. I also talk about the equidistribution of the intersection points between closed geodesics.<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar_2022-2023&diff=24231Dynamics Seminar 2022-20232023-01-22T21:02:13Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>During the Spring 2023 semester, the [[Dynamics]] seminar meets in room '''2425 of Sterling Hall''' on '''Mondays''' from '''2:30pm - 3:20pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host(s)<br />
|-<br />
|January 30<br />
|[http://websites.umich.edu/~blayac/ Pierre-Louis Blayac] (Michigan)<br />
|[[#Pierre-Louis Blayac| ''TBA'']]<br />
|Zhu and Zimmer<br />
|-<br />
|February 6<br />
|[http://www-personal.umich.edu/~kbutt/index.html Karen Butt] (Michigan)<br />
|Quantitative marked length spectrum rigidity<br />
|Zimmer<br />
|-<br />
|February 13<br />
|[https://sites.google.com/view/elizabeth-field Elizabeth Field] (Utah)<br />
|[[#Elizabeth Field| ''TBA'']]<br />
|Loving<br />
|-<br />
|February 20<br />
|[https://math.berkeley.edu/~chicheuk/ Chi Cheuk Tsang] (Berkeley)<br />
|[[#Chi Cheuk Tsang| ''Dilatations of pseudo-Anosov maps and standardly embedded train tracks'']]<br />
|Loving<br />
|-<br />
|February 27<br />
|[https://www.caglaruyanik.com/home Caglar Uyanik] (UW Madison)<br />
|[[#Caglar Uyanik| ''TBA'']]<br />
|local<br />
|-<br />
|March 6<br />
|[https://filippomazzoli.github.io Filippo Mazzoli] (UVA)<br />
|[[#Filippo Mazzoli| TBA]]<br />
|Zhu<br />
|-<br />
|March 13<br />
|Spring Break, No Seminar<br />
|<br />
|<br />
|-<br />
|March 20<br />
|[https://www.rosemorriswright.com/ Rose Morris-Wright ] (Middlebury)<br />
|[[#Rose Morris-Wright| ''TBA'']]<br />
|Dymarz<br />
|-<br />
|March 27<br />
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)<br />
|[[#Carolyn Abbott| ''TBA'']]<br />
|Dymarz and Uyanik<br />
|-<br />
|April 3<br />
|[https://sites.google.com/view/sfairchild/home Samantha Fairchild] (Osnabrück)<br />
|TBA<br />
|Apisa<br />
|-<br />
|April 10<br />
|[https://www.math.utah.edu/~chaika/ Jon Chaika] (Utah)<br />
|[[#Jon Chaika| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|April 17<br />
|[https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] (Chicago)<br />
|[[#Mikolaj Fraczyk| ''TBA'']]<br />
|Skenderi and Zimmer<br />
|-<br />
||April 24<br />
|[https://sites.google.com/view/tarikaougab/home/ Tarik Aougab] (Haverford)<br />
|[[#Tarik Aougab| ''TBA'']]<br />
|Loving<br />
|-<br />
|May 1<br />
|[https://www.dmartinezgranado.com Didac Martinez-Granado] (UC Davis)<br />
|[[#Didac Martinez-Granado| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Pierre-Louis Blayac===<br />
<br />
===Karen Butt===<br />
The marked length spectrum of a closed Riemannian manifold of negative curvature is a function on the free homotopy classes of closed curves which assigns to each class the length of its unique geodesic representative. It is known in certain cases that the marked length spectrum determines the metric up to isometry, and this is conjectured to be true in general. In this talk, we explore to what extent the marked length spectrum on a sufficiently large finite set approximately determines the metric.<br />
<br />
===Elizabeth Field===<br />
<br />
===Chi Cheuk Tsang===<br />
<br />
The dilatation of a pseudo-Anosov map is a measure of the complexity of its dynamics. The minimum dilatation problem asks for the minimum dilatation among all pseudo-Anosov maps defined on a fixed surface, which can be thought of as the smallest amount of mixing one can perform while still doing something topologically interesting. In this talk, we present some recent work on this problem with Eriko Hironaka, which shows a sharp lower bound for dilatations of fully-punctured pseudo-Anosov maps with at least two puncture orbits. We will explain some ideas in the proof, including standardly embedded train tracks and Perron-Frobenius matrices.<br />
<br />
===Caglar Uyanik===<br />
<br />
===Filippo Mazzoli===<br />
<br />
===Rose Morris-Wright===<br />
<br />
===Carolyn Abbott===<br />
<br />
===Samantha Fairchild===<br />
<br />
===Jon Chaika===<br />
<br />
===Mikolaj Fraczyk===<br />
<br />
===Tarik Aougab===<br />
<br />
===Didac Martinez-Granado===<br />
<br />
<br />
== Fall 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 12<br />
|[https://math.ou.edu/~jing/ Jing Tao] (OU)<br />
|[[#Jing Tao|Genericity of pseudo-Anosov maps]]<br />
|Dymarz and Uyanik<br />
|-<br />
|September 19<br />
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)(virtual)<br />
|[[#Rebekah Palmer|Totally geodesic surfaces in knot complements]]<br />
|VIRTUAL<br />
|-<br />
|September 26<br />
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)<br />
|[[#Beibei Liu|The critical exponent: old and new]]<br />
| Dymarz<br />
|-<br />
|October 3<br />
|Grace Work (UW-Madison)<br />
|[[#Grace Work |Discretely shrinking targets in moduli space]]<br />
|local<br />
|-<br />
|October 10<br />
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)<br />
|[[#Jean Pierre Mutanguha| Canonical forms for free group automorphisms]]<br />
|Uyanik<br />
|-<br />
|October 17<br />
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)<br />
|[[#Anthony Sanchez | Kontsevich-Zorich monodromy groups of translation covers of some platonic solids]]<br />
|Uyanik<br />
|-<br />
|October 24<br />
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (U Chicago)<br />
|postponed<br />
|Uyanik and Work<br />
|-<br />
|October 31<br />
|[https://sites.google.com/view/zhufeng-math/home Feng Zhu] (UW Madison)<br />
|[[#Feng Zhu| ''Relatively Anosov representations: a dynamical notion of geometric finiteness'']]<br />
|local<br />
|-<br />
|November 7<br />
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)<br />
|[[#Ethan Farber| ''Pseudo-Anosovs of interval type'']]<br />
|Loving<br />
|-<br />
|November 14<br />
|[https://www.math.montana.edu/geyer/ Lukas Geyer] (Montana) <br />
|[[#Lukas Geyer| ''Classification of critically fixed anti-Thurston maps'']]<br />
|Burkart<br />
|-<br />
|November 21<br />
|[http://www.hbaik.org/ Harry Hyungryul Baik] (KAIST)<br />
|[[#Harry Baik| ''Revisit the theory of laminar groups'']]<br />
|Wu<br />
|-<br />
|November 28<br />
|[https://mmontee.people.sites.carleton.edu MurphyKate Montee] (Carleton)<br />
|[[#MurphyKate Montee | ''Cubulation and Property (T) in random groups'']]<br />
|Dymarz<br />
|-<br />
|December 5<br />
|[https://sites.google.com/view/lovingmath/home Marissa Loving] (UW Madison)<br />
|[[#Marissa Loving|Unmarked simple length spectral rigidity for covers]]<br />
|local<br />
|-<br />
|December 12<br />
|[https://scholar.harvard.edu/tinatorkaman/home Tina Torkaman] (Harvard)<br />
|[[#Tina Torkaman| '' Intersection number and intersection points of closed geodesics on hyperbolic surfaces'']]<br />
|Uyanik<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Jing Tao===<br />
By Nielsen-Thurston classification, every homeomorphism of a surface is isotopic to one of three types: finite order, reducible, or pseudo-Anosov. While there are these three types, it is natural to wonder which type is more prevalent. In any reasonable way to sample matrices in SL(2,Z), irreducible matrices should be generic. One expects something similar for pseudo-Anosov maps. In joint work with Erlandsson and Souto, we define a notion of genericity and show that pseudo-Anosov maps are indeed generic. More precisely, we consider several "norms" on the mapping class group of the surface, and show that the proportion of pseudo-Anosov maps in a ball of radius r tends to 1 as r tends to infinity. The norms can be thought of as the natural analogues of matrix norms on SL(2,Z).<br />
<br />
===Rebekah Palmer===<br />
Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader--Fisher--Miller--Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case. In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces. On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover. This talk will explore this progress for both the uniqueness and the absence.<br />
<br />
===Beibei Liu===<br />
The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higher-rank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the Patterson-Sullivan theory and introduce new results about Kleinian groups with small or large critical exponents. <br />
<br />
===Grace Work===<br />
The shrinking target problem characterizes when there is a full measure set of points that hit a decreasing family of target sets under a given flow. This question is closely related to the Borel Cantilli lemma and also gives rise to logarithm laws. We will examine the discrete shrinking target problem in a general and then more specifically in the setting of Teichmuller flow on the moduli space of unit-area quadratic differentials.<br />
<br />
===Jean Pierre Mutanguha===<br />
The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!<br />
<br />
===Anthony Sanchez===<br />
Platonic solids have been studied for thousands of years. By unfolding a platonic solid we can associate to it a translation surface. Interesting information about the underlying platonic solid can be discovered in the cover where more (dynamical and geometric) structure is present. The translation covers we consider have a large group of symmetries that leave the global composition of the surface unchanged. However, the local structure of paths on the surface is often sensitive to these symmetries. The Kontsevich-Zorich mondromy group keeps track of this sensitivity. <br />
<br />
In joint work with R. Gutiérrez-Romo and D. Lee, we study the monodromy groups of translation covers of some platonic solids and show that the Zariski closure is a power of SL(2,R). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound").<br />
<br />
===Feng Zhu===<br />
<br />
Putting hyperbolic metrics on a finite-type surface S gives us linear representations of the fundamental group of S into PSL(2,R) with many nice geometric and dynamical properties: for instance they are discrete and faithful, and in fact stably quasi-isometrically embedded.<br />
<br />
In this talk, we will introduce (relatively) Anosov representations, which generalise this picture to higher-rank Lie groups such as PSL(d,R) for d>2, giving us a class of (relatively) hyperbolic subgroups there with similarly good geometric and dynamical properties.<br />
<br />
This is mostly joint work with Andrew Zimmer.<br />
<br />
===Ethan Farber===<br />
<br />
A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional topologists and dynamicists for the past forty years. We show that any pA on the sphere whose associated quadratic differential has at most one zero, admits an invariant train track whose expanding subgraph is an interval. Concretely, such a pA has the dynamics of an interval map. As an application, we recover a uniform lower bound on the entropy of these pAs originally due to Boissy-Lanneau. Time permitting, we will also discuss potential applications to a question of Fried. This is joint work with Karl Winsor.<br />
<br />
===Lukas Geyer===<br />
<br />
Recently there has been an increased interest in complex dynamics of orientation-reversing maps, in particular in the context of gravitational lensing and as an analogue of reflection groups in Sullivan's dictionary between Kleinian groups and dynamics of (anti-)rational maps. Much of the theory parallels the orientation-preserving case, but there are some intriguing differences. In order to deal with the post-critically finite case, we study anti-Thurston maps (orientation-reversing versions of Thurston maps), and prove an orientation-reversing analogue of Thurston's topological classification of post-critically finite rational maps, as well as the canonical decomposition of obstructed maps, following Pilgrim and Selinger. Using these tools, we obtain a combinatorial classification of critically fixed anti-Thurston maps, extending a recently obtained classification of critically fixed anti-rational maps. If time allows, I will explain applications of this classification to gravitational lensing. Most of this is based on joint work with Mikhail Hlushchanka.<br />
<br />
===Harry Baik ===<br />
<br />
I will give a brief introduction to laminar groups which are groups of orientation-preserving homeomorphisms of the circle admitting invariant laminations. The term was coined by Calegari and the study of laminar groups was motivated by work of Thurston and Calegari-Dunfield. We present old and new results on laminar groups which tell us when a given laminar group is either fuchsian or Kleinian. This is based on joint work with KyeongRo Kim and Hongtaek Jung.<br />
<br />
===MurphyKate Montee===<br />
<br />
Random groups are one way to study "typical" behavior of groups. In the Gromov density model, we often find that properties have a threshold density above which the property is satisfied with probability 1, and below which it is satisfied with probability 0. Two properties of random groups that have been well studied are cubulation (and relaxations of this property) and Property (T). In this setting these are mutually exclusive properties, but threshold densities are not known for either property. In this talk I'll present the current state of the art regarding these properties in random groups, and discuss some ways to further these results.<br />
<br />
===Marissa Loving===<br />
A fundamental question in geometry is the extent to which a manifold M is determined by its length spectrum, i.e. the collection of lengths of closed geodesics on M. This has been studied extensively for flat, hyperbolic, and negatively curved metrics. In this talk, we will focus on surfaces equipped with a choice of hyperbolic metric. We will explore the space between (1) work of Otal (resp. Fricke) which asserts that the marked length spectrum (resp. marked ''simple'' length spectrum) determines a hyperbolic surface, and (2) celebrated constructions of Vignéras and Sunada, which show that this rigidity fails when we forget the marking. In particular, we will consider the extent to which the unmarked simple length spectrum distinguishes between hyperbolic surfaces arising from Sunada’s construction. This represents joint work with Tarik Aougab, Max Lahn, and Nick Miller.<br />
<br />
===Tina Torkaman===<br />
<br />
In this talk, I will talk about the (geometric) intersection number between closed geodesics on finite volume hyperbolic surfaces. Specifically, I will discuss the optimum upper bound on the intersection number in terms of the product of hyperbolic lengths. I also talk about the equidistribution of the intersection points between closed geodesics.<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar_2022-2023&diff=24230Dynamics Seminar 2022-20232023-01-22T21:01:43Z<p>Amzimmer2: /* Karen Butt */</p>
<hr />
<div>During the Spring 2023 semester, the [[Dynamics]] seminar meets in room '''2425 of Sterling Hall''' on '''Mondays''' from '''2:30pm - 3:20pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, Chenxi Wu or Andy Zimmer. <br />
<br />
<br />
<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host(s)<br />
|-<br />
|January 30<br />
|[http://websites.umich.edu/~blayac/ Pierre-Louis Blayac] (Michigan)<br />
|[[#Pierre-Louis Blayac| ''TBA'']]<br />
|Zhu and Zimmer<br />
|-<br />
|February 6<br />
|[http://www-personal.umich.edu/~kbutt/index.html Karen Butt] (Michigan)<br />
|[[#Karen Butt| ''TBA'']]<br />
|Zimmer<br />
|-<br />
|February 13<br />
|[https://sites.google.com/view/elizabeth-field Elizabeth Field] (Utah)<br />
|[[#Elizabeth Field| ''TBA'']]<br />
|Loving<br />
|-<br />
|February 20<br />
|[https://math.berkeley.edu/~chicheuk/ Chi Cheuk Tsang] (Berkeley)<br />
|[[#Chi Cheuk Tsang| ''Dilatations of pseudo-Anosov maps and standardly embedded train tracks'']]<br />
|Loving<br />
|-<br />
|February 27<br />
|[https://www.caglaruyanik.com/home Caglar Uyanik] (UW Madison)<br />
|[[#Caglar Uyanik| ''TBA'']]<br />
|local<br />
|-<br />
|March 6<br />
|[https://filippomazzoli.github.io Filippo Mazzoli] (UVA)<br />
|[[#Filippo Mazzoli| TBA]]<br />
|Zhu<br />
|-<br />
|March 13<br />
|Spring Break, No Seminar<br />
|<br />
|<br />
|-<br />
|March 20<br />
|[https://www.rosemorriswright.com/ Rose Morris-Wright ] (Middlebury)<br />
|[[#Rose Morris-Wright| ''TBA'']]<br />
|Dymarz<br />
|-<br />
|March 27<br />
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)<br />
|[[#Carolyn Abbott| ''TBA'']]<br />
|Dymarz and Uyanik<br />
|-<br />
|April 3<br />
|[https://sites.google.com/view/sfairchild/home Samantha Fairchild] (Osnabrück)<br />
|TBA<br />
|Apisa<br />
|-<br />
|April 10<br />
|[https://www.math.utah.edu/~chaika/ Jon Chaika] (Utah)<br />
|[[#Jon Chaika| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|April 17<br />
|[https://sites.google.com/view/mikolaj-fraczyk/home Mikolaj Fraczyk] (Chicago)<br />
|[[#Mikolaj Fraczyk| ''TBA'']]<br />
|Skenderi and Zimmer<br />
|-<br />
||April 24<br />
|[https://sites.google.com/view/tarikaougab/home/ Tarik Aougab] (Haverford)<br />
|[[#Tarik Aougab| ''TBA'']]<br />
|Loving<br />
|-<br />
|May 1<br />
|[https://www.dmartinezgranado.com Didac Martinez-Granado] (UC Davis)<br />
|[[#Didac Martinez-Granado| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Pierre-Louis Blayac===<br />
<br />
===Karen Butt===<br />
The marked length spectrum of a closed Riemannian manifold of negative curvature is a function on the free homotopy classes of closed curves which assigns to each class the length of its unique geodesic representative. It is known in certain cases that the marked length spectrum determines the metric up to isometry, and this is conjectured to be true in general. In this talk, we explore to what extent the marked length spectrum on a sufficiently large finite set approximately determines the metric.<br />
<br />
===Elizabeth Field===<br />
<br />
===Chi Cheuk Tsang===<br />
<br />
The dilatation of a pseudo-Anosov map is a measure of the complexity of its dynamics. The minimum dilatation problem asks for the minimum dilatation among all pseudo-Anosov maps defined on a fixed surface, which can be thought of as the smallest amount of mixing one can perform while still doing something topologically interesting. In this talk, we present some recent work on this problem with Eriko Hironaka, which shows a sharp lower bound for dilatations of fully-punctured pseudo-Anosov maps with at least two puncture orbits. We will explain some ideas in the proof, including standardly embedded train tracks and Perron-Frobenius matrices.<br />
<br />
===Caglar Uyanik===<br />
<br />
===Filippo Mazzoli===<br />
<br />
===Rose Morris-Wright===<br />
<br />
===Carolyn Abbott===<br />
<br />
===Samantha Fairchild===<br />
<br />
===Jon Chaika===<br />
<br />
===Mikolaj Fraczyk===<br />
<br />
===Tarik Aougab===<br />
<br />
===Didac Martinez-Granado===<br />
<br />
<br />
== Fall 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 12<br />
|[https://math.ou.edu/~jing/ Jing Tao] (OU)<br />
|[[#Jing Tao|Genericity of pseudo-Anosov maps]]<br />
|Dymarz and Uyanik<br />
|-<br />
|September 19<br />
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)(virtual)<br />
|[[#Rebekah Palmer|Totally geodesic surfaces in knot complements]]<br />
|VIRTUAL<br />
|-<br />
|September 26<br />
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)<br />
|[[#Beibei Liu|The critical exponent: old and new]]<br />
| Dymarz<br />
|-<br />
|October 3<br />
|Grace Work (UW-Madison)<br />
|[[#Grace Work |Discretely shrinking targets in moduli space]]<br />
|local<br />
|-<br />
|October 10<br />
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)<br />
|[[#Jean Pierre Mutanguha| Canonical forms for free group automorphisms]]<br />
|Uyanik<br />
|-<br />
|October 17<br />
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)<br />
|[[#Anthony Sanchez | Kontsevich-Zorich monodromy groups of translation covers of some platonic solids]]<br />
|Uyanik<br />
|-<br />
|October 24<br />
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (U Chicago)<br />
|postponed<br />
|Uyanik and Work<br />
|-<br />
|October 31<br />
|[https://sites.google.com/view/zhufeng-math/home Feng Zhu] (UW Madison)<br />
|[[#Feng Zhu| ''Relatively Anosov representations: a dynamical notion of geometric finiteness'']]<br />
|local<br />
|-<br />
|November 7<br />
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)<br />
|[[#Ethan Farber| ''Pseudo-Anosovs of interval type'']]<br />
|Loving<br />
|-<br />
|November 14<br />
|[https://www.math.montana.edu/geyer/ Lukas Geyer] (Montana) <br />
|[[#Lukas Geyer| ''Classification of critically fixed anti-Thurston maps'']]<br />
|Burkart<br />
|-<br />
|November 21<br />
|[http://www.hbaik.org/ Harry Hyungryul Baik] (KAIST)<br />
|[[#Harry Baik| ''Revisit the theory of laminar groups'']]<br />
|Wu<br />
|-<br />
|November 28<br />
|[https://mmontee.people.sites.carleton.edu MurphyKate Montee] (Carleton)<br />
|[[#MurphyKate Montee | ''Cubulation and Property (T) in random groups'']]<br />
|Dymarz<br />
|-<br />
|December 5<br />
|[https://sites.google.com/view/lovingmath/home Marissa Loving] (UW Madison)<br />
|[[#Marissa Loving|Unmarked simple length spectral rigidity for covers]]<br />
|local<br />
|-<br />
|December 12<br />
|[https://scholar.harvard.edu/tinatorkaman/home Tina Torkaman] (Harvard)<br />
|[[#Tina Torkaman| '' Intersection number and intersection points of closed geodesics on hyperbolic surfaces'']]<br />
|Uyanik<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Jing Tao===<br />
By Nielsen-Thurston classification, every homeomorphism of a surface is isotopic to one of three types: finite order, reducible, or pseudo-Anosov. While there are these three types, it is natural to wonder which type is more prevalent. In any reasonable way to sample matrices in SL(2,Z), irreducible matrices should be generic. One expects something similar for pseudo-Anosov maps. In joint work with Erlandsson and Souto, we define a notion of genericity and show that pseudo-Anosov maps are indeed generic. More precisely, we consider several "norms" on the mapping class group of the surface, and show that the proportion of pseudo-Anosov maps in a ball of radius r tends to 1 as r tends to infinity. The norms can be thought of as the natural analogues of matrix norms on SL(2,Z).<br />
<br />
===Rebekah Palmer===<br />
Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader--Fisher--Miller--Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case. In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces. On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover. This talk will explore this progress for both the uniqueness and the absence.<br />
<br />
===Beibei Liu===<br />
The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higher-rank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the Patterson-Sullivan theory and introduce new results about Kleinian groups with small or large critical exponents. <br />
<br />
===Grace Work===<br />
The shrinking target problem characterizes when there is a full measure set of points that hit a decreasing family of target sets under a given flow. This question is closely related to the Borel Cantilli lemma and also gives rise to logarithm laws. We will examine the discrete shrinking target problem in a general and then more specifically in the setting of Teichmuller flow on the moduli space of unit-area quadratic differentials.<br />
<br />
===Jean Pierre Mutanguha===<br />
The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!<br />
<br />
===Anthony Sanchez===<br />
Platonic solids have been studied for thousands of years. By unfolding a platonic solid we can associate to it a translation surface. Interesting information about the underlying platonic solid can be discovered in the cover where more (dynamical and geometric) structure is present. The translation covers we consider have a large group of symmetries that leave the global composition of the surface unchanged. However, the local structure of paths on the surface is often sensitive to these symmetries. The Kontsevich-Zorich mondromy group keeps track of this sensitivity. <br />
<br />
In joint work with R. Gutiérrez-Romo and D. Lee, we study the monodromy groups of translation covers of some platonic solids and show that the Zariski closure is a power of SL(2,R). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound").<br />
<br />
===Feng Zhu===<br />
<br />
Putting hyperbolic metrics on a finite-type surface S gives us linear representations of the fundamental group of S into PSL(2,R) with many nice geometric and dynamical properties: for instance they are discrete and faithful, and in fact stably quasi-isometrically embedded.<br />
<br />
In this talk, we will introduce (relatively) Anosov representations, which generalise this picture to higher-rank Lie groups such as PSL(d,R) for d>2, giving us a class of (relatively) hyperbolic subgroups there with similarly good geometric and dynamical properties.<br />
<br />
This is mostly joint work with Andrew Zimmer.<br />
<br />
===Ethan Farber===<br />
<br />
A pseudo-Anosov (pA) is a homeomorphism of a compact connected surface S that, away from a finite set of points, acts locally as a linear map with one expanding and one contracting eigendirection. Ubiquitous yet mysterious, pAs have fascinated low-dimensional topologists and dynamicists for the past forty years. We show that any pA on the sphere whose associated quadratic differential has at most one zero, admits an invariant train track whose expanding subgraph is an interval. Concretely, such a pA has the dynamics of an interval map. As an application, we recover a uniform lower bound on the entropy of these pAs originally due to Boissy-Lanneau. Time permitting, we will also discuss potential applications to a question of Fried. This is joint work with Karl Winsor.<br />
<br />
===Lukas Geyer===<br />
<br />
Recently there has been an increased interest in complex dynamics of orientation-reversing maps, in particular in the context of gravitational lensing and as an analogue of reflection groups in Sullivan's dictionary between Kleinian groups and dynamics of (anti-)rational maps. Much of the theory parallels the orientation-preserving case, but there are some intriguing differences. In order to deal with the post-critically finite case, we study anti-Thurston maps (orientation-reversing versions of Thurston maps), and prove an orientation-reversing analogue of Thurston's topological classification of post-critically finite rational maps, as well as the canonical decomposition of obstructed maps, following Pilgrim and Selinger. Using these tools, we obtain a combinatorial classification of critically fixed anti-Thurston maps, extending a recently obtained classification of critically fixed anti-rational maps. If time allows, I will explain applications of this classification to gravitational lensing. Most of this is based on joint work with Mikhail Hlushchanka.<br />
<br />
===Harry Baik ===<br />
<br />
I will give a brief introduction to laminar groups which are groups of orientation-preserving homeomorphisms of the circle admitting invariant laminations. The term was coined by Calegari and the study of laminar groups was motivated by work of Thurston and Calegari-Dunfield. We present old and new results on laminar groups which tell us when a given laminar group is either fuchsian or Kleinian. This is based on joint work with KyeongRo Kim and Hongtaek Jung.<br />
<br />
===MurphyKate Montee===<br />
<br />
Random groups are one way to study "typical" behavior of groups. In the Gromov density model, we often find that properties have a threshold density above which the property is satisfied with probability 1, and below which it is satisfied with probability 0. Two properties of random groups that have been well studied are cubulation (and relaxations of this property) and Property (T). In this setting these are mutually exclusive properties, but threshold densities are not known for either property. In this talk I'll present the current state of the art regarding these properties in random groups, and discuss some ways to further these results.<br />
<br />
===Marissa Loving===<br />
A fundamental question in geometry is the extent to which a manifold M is determined by its length spectrum, i.e. the collection of lengths of closed geodesics on M. This has been studied extensively for flat, hyperbolic, and negatively curved metrics. In this talk, we will focus on surfaces equipped with a choice of hyperbolic metric. We will explore the space between (1) work of Otal (resp. Fricke) which asserts that the marked length spectrum (resp. marked ''simple'' length spectrum) determines a hyperbolic surface, and (2) celebrated constructions of Vignéras and Sunada, which show that this rigidity fails when we forget the marking. In particular, we will consider the extent to which the unmarked simple length spectrum distinguishes between hyperbolic surfaces arising from Sunada’s construction. This represents joint work with Tarik Aougab, Max Lahn, and Nick Miller.<br />
<br />
===Tina Torkaman===<br />
<br />
In this talk, I will talk about the (geometric) intersection number between closed geodesics on finite volume hyperbolic surfaces. Specifically, I will discuss the optimum upper bound on the intersection number in terms of the product of hyperbolic lengths. I also talk about the equidistribution of the intersection points between closed geodesics.<br />
<br />
<br />
<br />
<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar_2022-2023&diff=23784Dynamics Seminar 2022-20232022-09-30T18:01:54Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>The [[Dynamics]] seminar meets in room '''B329 of Van Vleck Hall''' on '''Mondays''' from '''2:30pm - 3:20pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, or Chenxi Wu. Contact Caglar Uyanik with your wisc email to get the zoom link for virtual talks. <br />
<br />
<br />
<br />
== Fall 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 12<br />
|[https://math.ou.edu/~jing/ Jing Tao] (OU)<br />
|[[#Jing Tao|Genericity of pseudo-Anosov maps]]<br />
|Dymarz and Uyanik<br />
|-<br />
|September 19<br />
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)(virtual)<br />
|[[#Rebekah Palmer|Totally geodesic surfaces in knot complements]]<br />
|VIRTUAL<br />
|-<br />
|September 26<br />
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)<br />
|[[#Beibei Liu|The critical exponent: old and new]]<br />
| Dymarz<br />
|-<br />
|October 3<br />
|Grace Work (UW-Madison)<br />
|[[#Grace Work |Discretely shrinking targets in moduli space]]<br />
|local<br />
|-<br />
|October 10<br />
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)<br />
|[[#Jean Pierre Mutanguha| Canonical forms for free group automorphisms]]<br />
|Uyanik<br />
|-<br />
|October 17<br />
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)<br />
|[[#Anthony Sanchez | Kontsevich-Zorich monodromy groups of translation covers of some platonic solids]]<br />
|Uyanik<br />
|-<br />
|October 24<br />
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (U Chicago)<br />
|[[#Alena Erchenko| ''TBA'']]<br />
|Uyanik and Work<br />
|-<br />
|October 31<br />
|[https://sites.google.com/view/zhufeng-math/home Feng Zhu] (UW Madison)<br />
|[[#Feng Zhu| ''TBA'']]<br />
|local<br />
|-<br />
|November 7<br />
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)<br />
|[[#Ethan Farber| ''TBA'']]<br />
|Loving<br />
|-<br />
|November 14<br />
|[https://www.math.montana.edu/geyer/ Lukas Geyer] (Montana) <br />
|[[#Lukas Geyer| ''TBA'']]<br />
|Burkart<br />
|-<br />
|November 21<br />
|[http://www.hbaik.org/ Harry Hyungryul Baik] (KAIST)<br />
|[[#Harry Baik| ''TBA'']]<br />
|Wu<br />
|-<br />
|November 28<br />
|[https://sites.google.com/view/lovingmath/home Marissa Loving] (UW Madison)<br />
|[[#Marissa Loving| ''TBA'']]<br />
|local<br />
|-<br />
|December 5<br />
|[https://mmontee.people.sites.carleton.edu MurphyKate Montee] (Carleton)<br />
|[[#MurphyKate Montee | ''TBA'']]<br />
|Dymarz<br />
|-<br />
|December 12<br />
|[https://scholar.harvard.edu/tinatorkaman/home Tina Torkaman] (Harvard)<br />
|[[#Tina Torkaman| ''TBA'']]<br />
|Uyanik<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Jing Tao===<br />
By Nielsen-Thurston classification, every homeomorphism of a surface is isotopic to one of three types: finite order, reducible, or pseudo-Anosov. While there are these three types, it is natural to wonder which type is more prevalent. In any reasonable way to sample matrices in SL(2,Z), irreducible matrices should be generic. One expects something similar for pseudo-Anosov maps. In joint work with Erlandsson and Souto, we define a notion of genericity and show that pseudo-Anosov maps are indeed generic. More precisely, we consider several "norms" on the mapping class group of the surface, and show that the proportion of pseudo-Anosov maps in a ball of radius r tends to 1 as r tends to infinity. The norms can be thought of as the natural analogues of matrix norms on SL(2,Z).<br />
<br />
===Rebekah Palmer===<br />
Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader--Fisher--Miller--Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case. In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces. On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover. This talk will explore this progress for both the uniqueness and the absence.<br />
<br />
===Beibei Liu===<br />
The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higher-rank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the Patterson-Sullivan theory and introduce new results about Kleinian groups with small or large critical exponents. <br />
<br />
===Grace Work===<br />
The shrinking target problem characterizes when there is a full measure set of points that hit a decreasing family of target sets under a given flow. This question is closely related to the Borel Cantilli lemma and also gives rise to logarithm laws. We will examine the discrete shrinking target problem in a general and then more specifically in the setting of Teichmuller flow on the moduli space of unit-area quadratic differentials.<br />
<br />
===Jean Pierre Mutanguha===<br />
The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!<br />
<br />
===Anthony Sanchez===<br />
Platonic solids have been studied for thousands of years. By unfolding a platonic solid we can associate to it a translation surface. Interesting information about the underlying platonic solid can be discovered in the cover where more (dynamical and geometric) structure is present. The translation covers we consider have a large group of symmetries that leave the global composition of the surface unchanged. However, the local structure of paths on the surface is often sensitive to these symmetries. The Kontsevich-Zorich mondromy group keeps track of this sensitivity. <br />
<br />
In joint work with R. Gutiérrez-Romo and D. Lee, we study the monodromy groups of translation covers of some platonic solids and show that the Zariski closure is a power of SL(2,R). We prove our results by finding generators for the monodromy groups, using a theorem of Matheus–Yoccoz–Zmiaikou that provides constraints on the Zariski closure of the groups (to obtain an "upper bound"), and analyzing the dimension of the Lie algebra of the Zariski closure of the group (to obtain a "lower bound").<br />
<br />
===Alena Erchenko===<br />
<br />
===Feng Zhu===<br />
<br />
===Ethan Farber===<br />
<br />
===Lukas Geyer===<br />
<br />
===Harry Baik ===<br />
<br />
===Marissa Loving===<br />
<br />
===MurphyKate Montee===<br />
<br />
===Tina Torkaman===<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host(s)<br />
|-<br />
|January 30<br />
|Pierre-Louis Blayac (Michigan)<br />
|[[TBA| ''TBA'']]<br />
|Zhu and Zimmer<br />
|-<br />
|February 6<br />
|[http://www-personal.umich.edu/~kbutt/index.html Karen Butt] (Michigan)<br />
|[[#Karen Butt| ''TBA'']]<br />
|Zimmer<br />
|-<br />
|March 27<br />
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)<br />
|[[#Carolyn Abbott| ''TBA'']]<br />
|Dymarz and Uyanik<br />
|-<br />
|April 10<br />
|[https://www.math.utah.edu/~chaika/ Jon Chaika] (Utah)<br />
|[[# Jon Chaika| ''TBA'']]<br />
|Apisa and Uyanik<br />
|-<br />
|April 24<br />
|[https://www.patelp.com Priyam Patel] (Utah)<br />
|[[#Priyam Patel| TBA]]<br />
|Loving and Uyanik<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Carolyn Abbott===<br />
<br />
===Priyam Patel ===<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Dynamics_Seminar_2022-2023&diff=23742Dynamics Seminar 2022-20232022-09-21T17:59:06Z<p>Amzimmer2: /* Spring 2023 */</p>
<hr />
<div>The [[Dynamics]] seminar meets in room '''B329 of Van Vleck Hall''' on '''Mondays''' from '''2:30pm - 3:20pm'''. To sign up for the mailing list send an email from your wisc.edu address to dynamics+join@g-groups.wisc.edu. For more information, contact Paul Apisa, Marissa Loving, Caglar Uyanik, or Chenxi Wu. Contact Caglar Uyanik with your wisc email to get the zoom link for virtual talks. <br />
<br />
<br />
<br />
== Fall 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
<br />
|-<br />
|September 12<br />
|[https://math.ou.edu/~jing/ Jing Tao] (OU)<br />
|[[#Jing Tao (OU) | Genericity of pseudo-Anosov maps]]<br />
|Dymarz and Uyanik<br />
|-<br />
|September 19<br />
|[https://math.temple.edu/~tug67058/ Rebekah Palmer] (Temple)(virtual)<br />
|[[# Rebekah Palmer (Temple)| Totally geodesic surfaces in knot complements]]<br />
|VIRTUAL<br />
|-<br />
|September 26<br />
|[https://sites.google.com/view/beibei-liu/ Beibei Liu] (MIT)<br />
|[[# Beibei Liu (Georgia Tech) |The critical exponent: old and new]]<br />
| Dymarz<br />
|-<br />
|October 3<br />
|Grace Work (UW-Madison)<br />
|[[# TBA | ''TBA'']]<br />
|local<br />
|-<br />
|October 10<br />
|[https://mutanguha.com/ Jean Pierre Mutanguha] (Princeton)<br />
|[[# Jean Pierre Mutanguha (Princeton) | ''TBA'']]<br />
|Uyanik<br />
|-<br />
|October 17<br />
|[https://sites.google.com/ucsd.edu/ans032/ Anthony Sanchez] (UCSD)<br />
|[[# Anthony Sanchez (UCSD)| ''TBA'']]<br />
|Uyanik<br />
|-<br />
|October 24<br />
|[https://you.stonybrook.edu/aerchenko/ Alena Erchenko] (U Chicago)<br />
|[[# Alena Erchenko| ''TBA'']]<br />
|Uyanik and Work<br />
|-<br />
|October 31<br />
|[https://sites.google.com/view/zhufeng-math/home Feng Zhu] (UW Madison)<br />
|[[# TBA| ''TBA'']]<br />
|local<br />
|-<br />
|November 7<br />
|[https://sites.google.com/bc.edu/ethan-farber/about-me?authuser=0/ Ethan Farber] (BC)<br />
|[[# Ethan Farber (BC)| ''TBA'']]<br />
|Loving<br />
|-<br />
|November 14<br />
|[https://www.math.montana.edu/geyer/ Lukas Geyer] (Montana) <br />
|[[# TBA| ''TBA'']]<br />
|Burkart<br />
|-<br />
|November 21<br />
|[http://www.hbaik.org/ Harry Hyungryul Baik] (KAIST)<br />
|[[# Harry Baik (KAIST)| ''TBA'']]<br />
|Wu<br />
|-<br />
|November 28<br />
|[https://sites.google.com/view/lovingmath/home Marissa Loving] (UW Madison)<br />
|[[# TBA| ''TBA'']]<br />
|local<br />
|-<br />
|December 5<br />
|[https://mmontee.people.sites.carleton.edu MurphyKate Montee] (Carleton)<br />
|[[# TBA| ''TBA'']]<br />
|Dymarz<br />
|-<br />
|December 12<br />
|[https://scholar.harvard.edu/tinatorkaman/home Tina Torkaman] (Harvard)<br />
|[[# TBA| ''TBA'']]<br />
|Uyanik<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Jing Tao===<br />
By Nielsen-Thurston classification, every homeomorphism of a surface is isotopic to one of three types: finite order, reducible, or pseudo-Anosov. While there are these three types, it is natural to wonder which type is more prevalent. In any reasonable way to sample matrices in SL(2,Z), irreducible matrices should be generic. One expects something similar for pseudo-Anosov maps. In joint work with Erlandsson and Souto, we define a notion of genericity and show that pseudo-Anosov maps are indeed generic. More precisely, we consider several "norms" on the mapping class group of the surface, and show that the proportion of pseudo-Anosov maps in a ball of radius r tends to 1 as r tends to infinity. The norms can be thought of as the natural analogues of matrix norms on SL(2,Z).<br />
<br />
===Rebekah Palmer===<br />
Studying totally geodesic surfaces has been essential in understanding the geometry and topology of hyperbolic 3-manifolds. Recently, Bader--Fisher--Miller--Stover showed that containing infinitely many such surfaces compels a manifold to be arithmetic. We are hence interested in counting totally geodesic surfaces in hyperbolic 3-manifolds in the finite (possibly zero) case. In joint work with Khánh Lê, we expand an obstruction, due to Calegari, to the existence of these surfaces. On the flipside, we prove the uniqueness of known totally geodesic surfaces by considering their behavior in the universal cover. This talk will explore this progress for both the uniqueness and the absence.<br />
<br />
===Beibei Liu===<br />
The critical exponent is an important numerical invariant of discrete groups acting on negatively curved Hadamard manifolds, Gromov hyperbolic spaces, and higher-rank symmetric spaces. In this talk, I will focus on discrete groups acting on hyperbolic spaces (i.e., Kleinian groups), which is a family of important examples of these three types of spaces. In particular, I will review the classical result relating the critical exponent to the Hausdorff dimension using the Patterson-Sullivan theory and introduce new results about Kleinian groups with small or large critical exponents. <br />
<br />
===Grace Work===<br />
<br />
===Jean Pierre Mutanguha===<br />
<br />
===Anthony Sanchez===<br />
<br />
===Alena Erchenko===<br />
<br />
===Feng Zhu===<br />
<br />
===Ethan Farber===<br />
<br />
===Lukas Geyer===<br />
<br />
===Harry Baik ===<br />
<br />
===Marissa Loving===<br />
<br />
===MurphyKate Montee===<br />
<br />
===Tina Torkaman===<br />
<br />
<br />
==Spring 2023==<br />
<br />
{| cellpadding="8"<br />
! align="left" |date<br />
! align="left" |speaker<br />
! align="left" |title<br />
! align="left" |host(s)<br />
|-<br />
|January 30<br />
|Pierre-Louis Blayac (Michigan)<br />
|[[TBA| ''TBA'']]<br />
|Zhu and Zimmer<br />
|-<br />
|March 27<br />
|[https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis)<br />
|[[# Carolyn Abbott (Brandeis) | ''TBA'']]<br />
|Dymarz and Uyanik<br />
|-<br />
|April 10<br />
|[https://www.math.utah.edu/~chaika/ Jon Chaika] (Utah)<br />
|[[# Jon Chaika (Utah) | ''TBA'']]<br />
|Apisa and Uyanik<br />
|-<br />
|April 24<br />
|[https://www.patelp.com Priyam Patel] (Utah)<br />
|[[# Priyam Patel (Utah) | TBA]]<br />
|Loving and Uyanik<br />
|}<br />
<br />
==Spring Abstracts==<br />
<br />
===Carolyn Abbott===<br />
<br />
===Priyam Patel ===<br />
<br />
== Archive of past Dynamics seminars==<br />
<br />
2021-2022 [[Dynamics_Seminar_2021-2022]]<br />
<br />
2020-2021 [[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar&diff=23015Geometry and Topology Seminar2022-03-24T00:34:17Z<p>Amzimmer2: /* =Matthew Stover */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:20pm''' (with some exceptions). For more information, contact Alex Waldron.<br />
<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan. 28<br />
|<br />
|Organizational meeting (includes graduate reading seminar)<br />
|-<br />
|Feb. 4<br />
|Daniel Stern (U Chicago)<br />
|Steklov-maximizing metrics on surfaces with many boundary components<br />
|-<br />
|Feb. 11<br />
|Autumn Kent (NOTE: starts at 1:00pm)<br />
|Deformations of hyperbolic manifolds and a theorem of Tian<br />
|-<br />
|Feb. 18<br />
|Alex Waldron<br />
|Strict type-II blowup in harmonic map flow<br />
|-<br />
|Mar. 4<br />
|Sean Paul<br />
|Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights<br />
|-<br />
|Mar. 11<br />
|Tian-Jun Li (U Minnesota, REMOTE)<br />
|Enhancing gauge theory invariants via generalized cohomologies<br />
|-<br />
|Mar. 25<br />
|Max Engelstein (U Minnesota)<br />
|Winding for Wave Maps<br />
|-<br />
|Apr. 8<br />
|Matthew Stover (Temple)<br />
|How to use, and prove, a superrigidity theorem<br />
|-<br />
|Apr. 15<br />
|Aleksander Doan (Columbia)<br />
|Holomorphic Floer theory and the Fueter equation<br />
|-<br />
|Apr. 22<br />
|McFeely Goodman (Berkeley)<br />
|<br />
|}<br />
<br />
== Spring abstracts ==<br />
<br />
===Daniel Stern===<br />
<br />
Just over a decade ago, Fraser and Schoen initiated the study of the maximization problem for the first Steklov eigenvalue among all metrics of fixed boundary length on a given compact surface. Drawing inspiration from the maximization problem for Laplace eigenvalues on closed surfaces–where extremal metrics are induced by minimal immersions into spheres–they showed that Steklov-maximizing metrics are induced by free boundary minimal immersions into Euclidean balls, and laid the groundwork for an existence theory (recently completed by Matthiesen-Petrides). In this talk, I’ll describe joint work with Mikhail Karpukhin, characterizing the limiting behavior of these metrics on surfaces of fixed genus g and k boundary components as k becomes large. In particular, I’ll explain why the associated free boundary minimal surfaces converge to the closed minimal surface of genus g in the sphere given by maximizing the first Laplace eigenvalue, with areas converging at a rate of (log k)/k.<br />
<br />
===Autumn Kent===<br />
<br />
(NOTE: talk will start at 1:00pm)<br />
<br />
A closed 3-manifold with pinched negative curvature admits a bona fide hyperbolic metric thanks to Perelman's proof of geometrization. Unfortunately, the proof doesn't tell us anything about the global geometry of the metric. An unpublished theorem of Tian says that if the curvature is very close to 1, the injectivity radius is bounded below, and a certain weighted L^2-norm of the traceless Ricci curvature is also small, then the metric is actually close to the unique hyperbolic metric up to third derivatives. The remarkable thing about his theorem is that there is no hypothesis on the volume.<br />
<br />
I'll talk about some applications of this theorem to hyperbolic geometry, which require a version of Tian's theorem that allows short curves, and why such a version should hold. This is joint work in progress with Ken Bromberg and Yair Minsky.<br />
<br />
===Alex Waldron===<br />
<br />
I'll describe some recent work on 2D harmonic map flow, in which I show that a familiar bound on the blowup rate at a finite-time singularity is sufficient for continuity of the body map. This is relevant to a conjecture of Topping.<br />
<br />
===Sean Paul===<br />
<br />
An interesting problem in complex differential geometry seeks to characterize the existence of a constant scalar curvature metric on a Hodge manifold in terms of the algebraic geometry of the underlying variety. The speaker has recently solved this problem for varieties with finite automorphism group. The talk aims to explain why the problem is interesting (and quite rich) and to describe in non-technical language the ideas in the title and how they all fit together.<br />
<br />
===Tian-Jun Li===<br />
<br />
(NOTE: This talk will be on zoom)<br />
<br />
I will describe a project with Mikio Furuta to enhance Gauge theory invariants using various generalized cohomology theories. This was motivated by the Bauer-Furuta stable cohomotopy Seiberg-Witten invariants.<br />
<br />
===Max Engelstein===<br />
<br />
Wave maps are harmonic maps from a Lorentzian domain to a<br />
Riemannian target. Like solutions to many energy critical PDE, wave maps<br />
can develop singularities where the energy concentrates on arbitrary<br />
small scales but the norm stays bounded. Zooming in on these<br />
singularities yields a harmonic map (called a soliton or bubble) in the<br />
weak limit. One fundamental question is whether this weak limit is<br />
unique, that is to say, whether different bubbles may appear as the<br />
limit of different sequences of rescalings.<br />
<br />
We show by example that uniqueness may not hold if the target manifold<br />
is not analytic. Our construction is heavily inspired by Peter<br />
Topping’s analogous example of a “winding” bubble in harmonic map heat<br />
flow. However, the Hamiltonian nature of the wave maps will occasionally<br />
necessitate different arguments. This is joint work with Dana Mendelson<br />
(U Chicago).<br />
<br />
===Matthew Stover===<br />
<br />
This talk will be about the engine behind my colloquium: a superrigidity theorem. I will start describing what a superrigidity theorem is, and how it relates to proving arithmeticitiy. I will also discuss some other applications of our superrigidity theorem to geometry. For example, if M is a finite-volume hyperbolic 3-manifold obtained by Dehn filling on another hyperbolic 3-manifold N, then only finitely many totally geodesic surfaces on N remain totally geodesic (up to isotopy) under the filling. For the rest of the talk, I will describe the main ingredients going into proving a superrigidity theorem, in particular an elegant formulation due to Bader and Furman.<br />
<br />
===Aleksander Doan===<br />
<br />
I will discuss an idea of constructing a category associated with a pair of holomorphic Lagrangian submanifolds in a hyperkahler manifold, or, more generally, a manifold equipped with a triple of almost complex structures I,J,K satisfying the quaternionic relation IJ =-JI= K. This putative category can be seen as an infinite-dimensional version of the Fukaya-Seidel category: a well-known invariant associated with a Lefschetz fibration (i.e. manifold with a complex Morse function). While many analytic aspects of this proposal remain unexplored, I will argue that in the case of the cotangent bundle of a Lefschetz fibration, our construction recovers the Fukaya-Seidel category. This talk is based on joint work with Semon Rezchikov, and builds on earlier ideas of Haydys, Gaiotto-Moore-Witten, and Kapranov-Kontsevich-Soibelman.<br />
<br />
== Fall 2021 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 10<br />
|<br />
|Organizational meeting<br />
|-<br />
|Sep. 17<br />
|Alex Waldron<br />
|Harmonic map flow for almost-holomorphic maps<br />
|-<br />
|Sep. 24<br />
|Sean Paul (Cancelled due to flight delay)<br />
|Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights<br />
|-<br />
|Oct. 1<br />
|Andrew Zimmer<br />
|Entropy rigidity old and new<br />
|-<br />
|Oct. 8<br />
|Laurentiu Maxim<br />
|Topology of complex projective hypersurfaces<br />
|-<br />
|Oct. 15<br />
|Gavin Ball<br />
|Introduction to G2 Geometry<br />
|-<br />
|Oct. 22<br />
|Chenxi Wu<br />
|Stable translation lengths on sphere graphs<br />
|-<br />
|Oct. 29<br />
|Brian Hepler (Note: seminar begins at 2:30 in VV B313)<br />
|Vanishing Cycles for Irregular Local Systems<br />
|-<br />
|Nov. 5<br />
|Botong Wang<br />
|Topological methods in combinatorics<br />
|-<br />
|Nov. 12<br />
|Nate Fisher<br />
|Horofunction boundaries of groups and spaces<br />
|-<br />
|Nov. 19<br />
|Sigurd Angenent<br />
|Questions for Topologists about Curve Shortening<br />
|-<br />
|Dec. 3<br />
|Pei-Ken Hung (U Minnesota)<br />
|Toroidal positive mass theorem<br />
|-<br />
|Dec. 10<br />
|Nianzi Li<br />
|Asymptotic metrics on the moduli spaces of Higgs bundles<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Waldron===<br />
<br />
I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.<br />
<br />
===Sean Paul===<br />
<br />
(See Spring semester)<br />
<br />
===Andrew Zimmer===<br />
<br />
Informally, an "entropy rigidity" result characterizes some special geometric object (e.g. a constant curvature metric on a manifold) as a maximizer/minimizer of some function of the objects asymptotic complexity. In this talk I will survey some classical entropy rigidity results in hyperbolic and Riemannian geometry. Then, if time allows, I will discuss some recent joint work with Canary and Zhang. The talk should be accessible to first year graduate students.<br />
<br />
===Laurentiu Maxim===<br />
<br />
I will overview old and new results which show how the presence of singularities affects the topology of complex projective hypersurfaces.<br />
<br />
===Gavin Ball===<br />
<br />
I will give an introduction to the theory of manifolds with holonomy group G2. I will begin by describing the exceptional Lie group G2 using some special linear algebra in dimension 7. Then I will give an overview of the holonomy group of a Riemannian manifold and describe Berger's classification theorem. The group G2 is one of two exceptional members of Berger's list, and I will explain the interesting properties manifolds with holonomy G2 have and sketch the construction of examples. If time permits, I will describe some of my recent work on manifolds with closed G2-structure.<br />
<br />
===Chenxi Wu===<br />
<br />
I will discuss some of my prior works in collaboration with Harry Baik, Dongryul Kim, Hyunshik Shin and Eiko Kin on stable translation lengths on sphere graphs for maps in a fibered cone, and discuss the applications on maps on surfaces, finite graphs and handlebody groups.<br />
<br />
===Brian Hepler===<br />
<br />
We give a generalization of the notion of vanishing cycles to the setting of enhanced ind-sheaves on to any complex manifold X and holomorphic function f : X → C. Specifically, we show that there are two distinct (but Verdier-dual) functors, denoted φ+∞ and φ−∞, that deserve the name of “irregular” vanishing cycles associated to such a function f : X → C. Loosely, these functors capture the two distinct ways in which an irregular local system on the complement of the hypersurface V(f) can be extended across that hypersurface.<br />
<br />
Note: due to teaching conflict, Brian's talk will start at 2:30 in Van Vleck B313.<br />
<br />
===Botong Wang===<br />
<br />
We will give a survey of two results from combinatorics: the Heron-Rota-Welsh conjecture about the log-concavity of the coefficients of chromatic polynomials and the Top-heavy conjecture by Dowling-Wilson on the number of subspaces spanned by a finite set of vectors in a vector space. I will explain how topological and algebra-geometric methods can be relevant to such problems and how one can replace geometric arguments by combinatorial ones to extend the conclusions to non-realizable objects.<br />
<br />
===Nate Fisher===<br />
<br />
In this talk, I will define and motivate the use of horofunction boundaries in the study of groups. I will go through some examples, discuss how the horofunction boundary is related to other boundary theories, and survey a few applications of horofunction boundary.<br />
<br />
===Sigurd Angenent===<br />
<br />
Curve Shortening is the simplest and most easy to visualize of the geometric flows that have been considered in the past few decades. Nevertheless there are many open questions about the kind of singularities that can appear in CS, and several of these questions probably, hopefully, have topological answers. I'll give a short overview of what is and what isn't known. While geometric flows have had success in solving old problems in topology (Poincaré conjecture, etc.) , I would like turn things around in my talk and argue that rather than asking what analysis can do for topology, we should ask what topology can do for analysis.<br />
<br />
===Pei-Ken Hung===<br />
<br />
We establish the positive mass theorem for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity. In the umbilic case, a rigidity statement is proven showing that the total mass vanishes precisely when the initial data manifold is isometric to a portion of the canonical slice of the associated Kottler spacetime. Furthermore, we provide a new proof of the recent rigidity theorems of Eichmair-Galloway-Mendes in dimension 3, with weakened hypotheses in certain cases. These results are obtained through an analysis of the level sets of spacetime harmonic functions. This is a joint work with Aghil Alaee and Marcus Khuri.<br />
<br />
===Nianzi Li===<br />
<br />
I will introduce the definition of Higgs bundles, discuss some structures and metrics on the moduli spaces of Higgs bundles. Then I will give an overview of the results of Mazzeo-Swoboda-Weiss-Witt and Fredrickson on the exponential decay of the difference between the hyperkähler L^2 metric and the semi-flat metric along a generic ray. Finally, I will briefly talk about Boalch's modularity conjecture, and describe an ongoing work of extending the results to Higgs bundles with irregular singularities on a Riemann sphere, some of the moduli spaces are shown to be ALG gravitational instantons.<br />
<br />
== Archive of past Geometry seminars ==<br />
2020-2021 [[Geometry_and_Topology_Seminar_2020-2021]]<br />
<br><br><br />
2019-2020 [[Geometry_and_Topology_Seminar_2019-2020]]<br />
<br><br><br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
[[Fall-2010-Geometry-Topology]]<br><br />
[[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar&diff=23014Geometry and Topology Seminar2022-03-24T00:34:08Z<p>Amzimmer2: /* Spring abstracts */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:20pm''' (with some exceptions). For more information, contact Alex Waldron.<br />
<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan. 28<br />
|<br />
|Organizational meeting (includes graduate reading seminar)<br />
|-<br />
|Feb. 4<br />
|Daniel Stern (U Chicago)<br />
|Steklov-maximizing metrics on surfaces with many boundary components<br />
|-<br />
|Feb. 11<br />
|Autumn Kent (NOTE: starts at 1:00pm)<br />
|Deformations of hyperbolic manifolds and a theorem of Tian<br />
|-<br />
|Feb. 18<br />
|Alex Waldron<br />
|Strict type-II blowup in harmonic map flow<br />
|-<br />
|Mar. 4<br />
|Sean Paul<br />
|Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights<br />
|-<br />
|Mar. 11<br />
|Tian-Jun Li (U Minnesota, REMOTE)<br />
|Enhancing gauge theory invariants via generalized cohomologies<br />
|-<br />
|Mar. 25<br />
|Max Engelstein (U Minnesota)<br />
|Winding for Wave Maps<br />
|-<br />
|Apr. 8<br />
|Matthew Stover (Temple)<br />
|How to use, and prove, a superrigidity theorem<br />
|-<br />
|Apr. 15<br />
|Aleksander Doan (Columbia)<br />
|Holomorphic Floer theory and the Fueter equation<br />
|-<br />
|Apr. 22<br />
|McFeely Goodman (Berkeley)<br />
|<br />
|}<br />
<br />
== Spring abstracts ==<br />
<br />
===Daniel Stern===<br />
<br />
Just over a decade ago, Fraser and Schoen initiated the study of the maximization problem for the first Steklov eigenvalue among all metrics of fixed boundary length on a given compact surface. Drawing inspiration from the maximization problem for Laplace eigenvalues on closed surfaces–where extremal metrics are induced by minimal immersions into spheres–they showed that Steklov-maximizing metrics are induced by free boundary minimal immersions into Euclidean balls, and laid the groundwork for an existence theory (recently completed by Matthiesen-Petrides). In this talk, I’ll describe joint work with Mikhail Karpukhin, characterizing the limiting behavior of these metrics on surfaces of fixed genus g and k boundary components as k becomes large. In particular, I’ll explain why the associated free boundary minimal surfaces converge to the closed minimal surface of genus g in the sphere given by maximizing the first Laplace eigenvalue, with areas converging at a rate of (log k)/k.<br />
<br />
===Autumn Kent===<br />
<br />
(NOTE: talk will start at 1:00pm)<br />
<br />
A closed 3-manifold with pinched negative curvature admits a bona fide hyperbolic metric thanks to Perelman's proof of geometrization. Unfortunately, the proof doesn't tell us anything about the global geometry of the metric. An unpublished theorem of Tian says that if the curvature is very close to 1, the injectivity radius is bounded below, and a certain weighted L^2-norm of the traceless Ricci curvature is also small, then the metric is actually close to the unique hyperbolic metric up to third derivatives. The remarkable thing about his theorem is that there is no hypothesis on the volume.<br />
<br />
I'll talk about some applications of this theorem to hyperbolic geometry, which require a version of Tian's theorem that allows short curves, and why such a version should hold. This is joint work in progress with Ken Bromberg and Yair Minsky.<br />
<br />
===Alex Waldron===<br />
<br />
I'll describe some recent work on 2D harmonic map flow, in which I show that a familiar bound on the blowup rate at a finite-time singularity is sufficient for continuity of the body map. This is relevant to a conjecture of Topping.<br />
<br />
===Sean Paul===<br />
<br />
An interesting problem in complex differential geometry seeks to characterize the existence of a constant scalar curvature metric on a Hodge manifold in terms of the algebraic geometry of the underlying variety. The speaker has recently solved this problem for varieties with finite automorphism group. The talk aims to explain why the problem is interesting (and quite rich) and to describe in non-technical language the ideas in the title and how they all fit together.<br />
<br />
===Tian-Jun Li===<br />
<br />
(NOTE: This talk will be on zoom)<br />
<br />
I will describe a project with Mikio Furuta to enhance Gauge theory invariants using various generalized cohomology theories. This was motivated by the Bauer-Furuta stable cohomotopy Seiberg-Witten invariants.<br />
<br />
===Max Engelstein===<br />
<br />
Wave maps are harmonic maps from a Lorentzian domain to a<br />
Riemannian target. Like solutions to many energy critical PDE, wave maps<br />
can develop singularities where the energy concentrates on arbitrary<br />
small scales but the norm stays bounded. Zooming in on these<br />
singularities yields a harmonic map (called a soliton or bubble) in the<br />
weak limit. One fundamental question is whether this weak limit is<br />
unique, that is to say, whether different bubbles may appear as the<br />
limit of different sequences of rescalings.<br />
<br />
We show by example that uniqueness may not hold if the target manifold<br />
is not analytic. Our construction is heavily inspired by Peter<br />
Topping’s analogous example of a “winding” bubble in harmonic map heat<br />
flow. However, the Hamiltonian nature of the wave maps will occasionally<br />
necessitate different arguments. This is joint work with Dana Mendelson<br />
(U Chicago).<br />
<br />
===Matthew Stover==<br />
<br />
This talk will be about the engine behind my colloquium: a superrigidity theorem. I will start describing what a superrigidity theorem is, and how it relates to proving arithmeticitiy. I will also discuss some other applications of our superrigidity theorem to geometry. For example, if M is a finite-volume hyperbolic 3-manifold obtained by Dehn filling on another hyperbolic 3-manifold N, then only finitely many totally geodesic surfaces on N remain totally geodesic (up to isotopy) under the filling. For the rest of the talk, I will describe the main ingredients going into proving a superrigidity theorem, in particular an elegant formulation due to Bader and Furman.<br />
<br />
===Aleksander Doan===<br />
<br />
I will discuss an idea of constructing a category associated with a pair of holomorphic Lagrangian submanifolds in a hyperkahler manifold, or, more generally, a manifold equipped with a triple of almost complex structures I,J,K satisfying the quaternionic relation IJ =-JI= K. This putative category can be seen as an infinite-dimensional version of the Fukaya-Seidel category: a well-known invariant associated with a Lefschetz fibration (i.e. manifold with a complex Morse function). While many analytic aspects of this proposal remain unexplored, I will argue that in the case of the cotangent bundle of a Lefschetz fibration, our construction recovers the Fukaya-Seidel category. This talk is based on joint work with Semon Rezchikov, and builds on earlier ideas of Haydys, Gaiotto-Moore-Witten, and Kapranov-Kontsevich-Soibelman.<br />
<br />
== Fall 2021 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 10<br />
|<br />
|Organizational meeting<br />
|-<br />
|Sep. 17<br />
|Alex Waldron<br />
|Harmonic map flow for almost-holomorphic maps<br />
|-<br />
|Sep. 24<br />
|Sean Paul (Cancelled due to flight delay)<br />
|Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights<br />
|-<br />
|Oct. 1<br />
|Andrew Zimmer<br />
|Entropy rigidity old and new<br />
|-<br />
|Oct. 8<br />
|Laurentiu Maxim<br />
|Topology of complex projective hypersurfaces<br />
|-<br />
|Oct. 15<br />
|Gavin Ball<br />
|Introduction to G2 Geometry<br />
|-<br />
|Oct. 22<br />
|Chenxi Wu<br />
|Stable translation lengths on sphere graphs<br />
|-<br />
|Oct. 29<br />
|Brian Hepler (Note: seminar begins at 2:30 in VV B313)<br />
|Vanishing Cycles for Irregular Local Systems<br />
|-<br />
|Nov. 5<br />
|Botong Wang<br />
|Topological methods in combinatorics<br />
|-<br />
|Nov. 12<br />
|Nate Fisher<br />
|Horofunction boundaries of groups and spaces<br />
|-<br />
|Nov. 19<br />
|Sigurd Angenent<br />
|Questions for Topologists about Curve Shortening<br />
|-<br />
|Dec. 3<br />
|Pei-Ken Hung (U Minnesota)<br />
|Toroidal positive mass theorem<br />
|-<br />
|Dec. 10<br />
|Nianzi Li<br />
|Asymptotic metrics on the moduli spaces of Higgs bundles<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Waldron===<br />
<br />
I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.<br />
<br />
===Sean Paul===<br />
<br />
(See Spring semester)<br />
<br />
===Andrew Zimmer===<br />
<br />
Informally, an "entropy rigidity" result characterizes some special geometric object (e.g. a constant curvature metric on a manifold) as a maximizer/minimizer of some function of the objects asymptotic complexity. In this talk I will survey some classical entropy rigidity results in hyperbolic and Riemannian geometry. Then, if time allows, I will discuss some recent joint work with Canary and Zhang. The talk should be accessible to first year graduate students.<br />
<br />
===Laurentiu Maxim===<br />
<br />
I will overview old and new results which show how the presence of singularities affects the topology of complex projective hypersurfaces.<br />
<br />
===Gavin Ball===<br />
<br />
I will give an introduction to the theory of manifolds with holonomy group G2. I will begin by describing the exceptional Lie group G2 using some special linear algebra in dimension 7. Then I will give an overview of the holonomy group of a Riemannian manifold and describe Berger's classification theorem. The group G2 is one of two exceptional members of Berger's list, and I will explain the interesting properties manifolds with holonomy G2 have and sketch the construction of examples. If time permits, I will describe some of my recent work on manifolds with closed G2-structure.<br />
<br />
===Chenxi Wu===<br />
<br />
I will discuss some of my prior works in collaboration with Harry Baik, Dongryul Kim, Hyunshik Shin and Eiko Kin on stable translation lengths on sphere graphs for maps in a fibered cone, and discuss the applications on maps on surfaces, finite graphs and handlebody groups.<br />
<br />
===Brian Hepler===<br />
<br />
We give a generalization of the notion of vanishing cycles to the setting of enhanced ind-sheaves on to any complex manifold X and holomorphic function f : X → C. Specifically, we show that there are two distinct (but Verdier-dual) functors, denoted φ+∞ and φ−∞, that deserve the name of “irregular” vanishing cycles associated to such a function f : X → C. Loosely, these functors capture the two distinct ways in which an irregular local system on the complement of the hypersurface V(f) can be extended across that hypersurface.<br />
<br />
Note: due to teaching conflict, Brian's talk will start at 2:30 in Van Vleck B313.<br />
<br />
===Botong Wang===<br />
<br />
We will give a survey of two results from combinatorics: the Heron-Rota-Welsh conjecture about the log-concavity of the coefficients of chromatic polynomials and the Top-heavy conjecture by Dowling-Wilson on the number of subspaces spanned by a finite set of vectors in a vector space. I will explain how topological and algebra-geometric methods can be relevant to such problems and how one can replace geometric arguments by combinatorial ones to extend the conclusions to non-realizable objects.<br />
<br />
===Nate Fisher===<br />
<br />
In this talk, I will define and motivate the use of horofunction boundaries in the study of groups. I will go through some examples, discuss how the horofunction boundary is related to other boundary theories, and survey a few applications of horofunction boundary.<br />
<br />
===Sigurd Angenent===<br />
<br />
Curve Shortening is the simplest and most easy to visualize of the geometric flows that have been considered in the past few decades. Nevertheless there are many open questions about the kind of singularities that can appear in CS, and several of these questions probably, hopefully, have topological answers. I'll give a short overview of what is and what isn't known. While geometric flows have had success in solving old problems in topology (Poincaré conjecture, etc.) , I would like turn things around in my talk and argue that rather than asking what analysis can do for topology, we should ask what topology can do for analysis.<br />
<br />
===Pei-Ken Hung===<br />
<br />
We establish the positive mass theorem for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity. In the umbilic case, a rigidity statement is proven showing that the total mass vanishes precisely when the initial data manifold is isometric to a portion of the canonical slice of the associated Kottler spacetime. Furthermore, we provide a new proof of the recent rigidity theorems of Eichmair-Galloway-Mendes in dimension 3, with weakened hypotheses in certain cases. These results are obtained through an analysis of the level sets of spacetime harmonic functions. This is a joint work with Aghil Alaee and Marcus Khuri.<br />
<br />
===Nianzi Li===<br />
<br />
I will introduce the definition of Higgs bundles, discuss some structures and metrics on the moduli spaces of Higgs bundles. Then I will give an overview of the results of Mazzeo-Swoboda-Weiss-Witt and Fredrickson on the exponential decay of the difference between the hyperkähler L^2 metric and the semi-flat metric along a generic ray. Finally, I will briefly talk about Boalch's modularity conjecture, and describe an ongoing work of extending the results to Higgs bundles with irregular singularities on a Riemann sphere, some of the moduli spaces are shown to be ALG gravitational instantons.<br />
<br />
== Archive of past Geometry seminars ==<br />
2020-2021 [[Geometry_and_Topology_Seminar_2020-2021]]<br />
<br><br><br />
2019-2020 [[Geometry_and_Topology_Seminar_2019-2020]]<br />
<br><br><br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
[[Fall-2010-Geometry-Topology]]<br><br />
[[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar&diff=23013Geometry and Topology Seminar2022-03-24T00:33:23Z<p>Amzimmer2: /* Spring 2022 */</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:20pm''' (with some exceptions). For more information, contact Alex Waldron.<br />
<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2022 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Jan. 28<br />
|<br />
|Organizational meeting (includes graduate reading seminar)<br />
|-<br />
|Feb. 4<br />
|Daniel Stern (U Chicago)<br />
|Steklov-maximizing metrics on surfaces with many boundary components<br />
|-<br />
|Feb. 11<br />
|Autumn Kent (NOTE: starts at 1:00pm)<br />
|Deformations of hyperbolic manifolds and a theorem of Tian<br />
|-<br />
|Feb. 18<br />
|Alex Waldron<br />
|Strict type-II blowup in harmonic map flow<br />
|-<br />
|Mar. 4<br />
|Sean Paul<br />
|Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights<br />
|-<br />
|Mar. 11<br />
|Tian-Jun Li (U Minnesota, REMOTE)<br />
|Enhancing gauge theory invariants via generalized cohomologies<br />
|-<br />
|Mar. 25<br />
|Max Engelstein (U Minnesota)<br />
|Winding for Wave Maps<br />
|-<br />
|Apr. 8<br />
|Matthew Stover (Temple)<br />
|How to use, and prove, a superrigidity theorem<br />
|-<br />
|Apr. 15<br />
|Aleksander Doan (Columbia)<br />
|Holomorphic Floer theory and the Fueter equation<br />
|-<br />
|Apr. 22<br />
|McFeely Goodman (Berkeley)<br />
|<br />
|}<br />
<br />
== Spring abstracts ==<br />
<br />
===Daniel Stern===<br />
<br />
Just over a decade ago, Fraser and Schoen initiated the study of the maximization problem for the first Steklov eigenvalue among all metrics of fixed boundary length on a given compact surface. Drawing inspiration from the maximization problem for Laplace eigenvalues on closed surfaces–where extremal metrics are induced by minimal immersions into spheres–they showed that Steklov-maximizing metrics are induced by free boundary minimal immersions into Euclidean balls, and laid the groundwork for an existence theory (recently completed by Matthiesen-Petrides). In this talk, I’ll describe joint work with Mikhail Karpukhin, characterizing the limiting behavior of these metrics on surfaces of fixed genus g and k boundary components as k becomes large. In particular, I’ll explain why the associated free boundary minimal surfaces converge to the closed minimal surface of genus g in the sphere given by maximizing the first Laplace eigenvalue, with areas converging at a rate of (log k)/k.<br />
<br />
===Autumn Kent===<br />
<br />
(NOTE: talk will start at 1:00pm)<br />
<br />
A closed 3-manifold with pinched negative curvature admits a bona fide hyperbolic metric thanks to Perelman's proof of geometrization. Unfortunately, the proof doesn't tell us anything about the global geometry of the metric. An unpublished theorem of Tian says that if the curvature is very close to 1, the injectivity radius is bounded below, and a certain weighted L^2-norm of the traceless Ricci curvature is also small, then the metric is actually close to the unique hyperbolic metric up to third derivatives. The remarkable thing about his theorem is that there is no hypothesis on the volume.<br />
<br />
I'll talk about some applications of this theorem to hyperbolic geometry, which require a version of Tian's theorem that allows short curves, and why such a version should hold. This is joint work in progress with Ken Bromberg and Yair Minsky.<br />
<br />
===Alex Waldron===<br />
<br />
I'll describe some recent work on 2D harmonic map flow, in which I show that a familiar bound on the blowup rate at a finite-time singularity is sufficient for continuity of the body map. This is relevant to a conjecture of Topping.<br />
<br />
===Sean Paul===<br />
<br />
An interesting problem in complex differential geometry seeks to characterize the existence of a constant scalar curvature metric on a Hodge manifold in terms of the algebraic geometry of the underlying variety. The speaker has recently solved this problem for varieties with finite automorphism group. The talk aims to explain why the problem is interesting (and quite rich) and to describe in non-technical language the ideas in the title and how they all fit together.<br />
<br />
===Tian-Jun Li===<br />
<br />
(NOTE: This talk will be on zoom)<br />
<br />
I will describe a project with Mikio Furuta to enhance Gauge theory invariants using various generalized cohomology theories. This was motivated by the Bauer-Furuta stable cohomotopy Seiberg-Witten invariants.<br />
<br />
===Max Engelstein===<br />
<br />
Wave maps are harmonic maps from a Lorentzian domain to a<br />
Riemannian target. Like solutions to many energy critical PDE, wave maps<br />
can develop singularities where the energy concentrates on arbitrary<br />
small scales but the norm stays bounded. Zooming in on these<br />
singularities yields a harmonic map (called a soliton or bubble) in the<br />
weak limit. One fundamental question is whether this weak limit is<br />
unique, that is to say, whether different bubbles may appear as the<br />
limit of different sequences of rescalings.<br />
<br />
We show by example that uniqueness may not hold if the target manifold<br />
is not analytic. Our construction is heavily inspired by Peter<br />
Topping’s analogous example of a “winding” bubble in harmonic map heat<br />
flow. However, the Hamiltonian nature of the wave maps will occasionally<br />
necessitate different arguments. This is joint work with Dana Mendelson<br />
(U Chicago).<br />
<br />
===Aleksander Doan===<br />
<br />
I will discuss an idea of constructing a category associated with a pair of holomorphic Lagrangian submanifolds in a hyperkahler manifold, or, more generally, a manifold equipped with a triple of almost complex structures I,J,K satisfying the quaternionic relation IJ =-JI= K. This putative category can be seen as an infinite-dimensional version of the Fukaya-Seidel category: a well-known invariant associated with a Lefschetz fibration (i.e. manifold with a complex Morse function). While many analytic aspects of this proposal remain unexplored, I will argue that in the case of the cotangent bundle of a Lefschetz fibration, our construction recovers the Fukaya-Seidel category. This talk is based on joint work with Semon Rezchikov, and builds on earlier ideas of Haydys, Gaiotto-Moore-Witten, and Kapranov-Kontsevich-Soibelman.<br />
<br />
== Fall 2021 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
|-<br />
|Sep. 10<br />
|<br />
|Organizational meeting<br />
|-<br />
|Sep. 17<br />
|Alex Waldron<br />
|Harmonic map flow for almost-holomorphic maps<br />
|-<br />
|Sep. 24<br />
|Sean Paul (Cancelled due to flight delay)<br />
|Geometric Invariant Theory, Stable Pairs, Canonical Kähler metrics & Heights<br />
|-<br />
|Oct. 1<br />
|Andrew Zimmer<br />
|Entropy rigidity old and new<br />
|-<br />
|Oct. 8<br />
|Laurentiu Maxim<br />
|Topology of complex projective hypersurfaces<br />
|-<br />
|Oct. 15<br />
|Gavin Ball<br />
|Introduction to G2 Geometry<br />
|-<br />
|Oct. 22<br />
|Chenxi Wu<br />
|Stable translation lengths on sphere graphs<br />
|-<br />
|Oct. 29<br />
|Brian Hepler (Note: seminar begins at 2:30 in VV B313)<br />
|Vanishing Cycles for Irregular Local Systems<br />
|-<br />
|Nov. 5<br />
|Botong Wang<br />
|Topological methods in combinatorics<br />
|-<br />
|Nov. 12<br />
|Nate Fisher<br />
|Horofunction boundaries of groups and spaces<br />
|-<br />
|Nov. 19<br />
|Sigurd Angenent<br />
|Questions for Topologists about Curve Shortening<br />
|-<br />
|Dec. 3<br />
|Pei-Ken Hung (U Minnesota)<br />
|Toroidal positive mass theorem<br />
|-<br />
|Dec. 10<br />
|Nianzi Li<br />
|Asymptotic metrics on the moduli spaces of Higgs bundles<br />
|-<br />
|}<br />
<br />
== Fall Abstracts ==<br />
<br />
===Alex Waldron===<br />
<br />
I'll describe some history, recent results, and open problems about harmonic map flow, particularly in the 2-dimensional case.<br />
<br />
===Sean Paul===<br />
<br />
(See Spring semester)<br />
<br />
===Andrew Zimmer===<br />
<br />
Informally, an "entropy rigidity" result characterizes some special geometric object (e.g. a constant curvature metric on a manifold) as a maximizer/minimizer of some function of the objects asymptotic complexity. In this talk I will survey some classical entropy rigidity results in hyperbolic and Riemannian geometry. Then, if time allows, I will discuss some recent joint work with Canary and Zhang. The talk should be accessible to first year graduate students.<br />
<br />
===Laurentiu Maxim===<br />
<br />
I will overview old and new results which show how the presence of singularities affects the topology of complex projective hypersurfaces.<br />
<br />
===Gavin Ball===<br />
<br />
I will give an introduction to the theory of manifolds with holonomy group G2. I will begin by describing the exceptional Lie group G2 using some special linear algebra in dimension 7. Then I will give an overview of the holonomy group of a Riemannian manifold and describe Berger's classification theorem. The group G2 is one of two exceptional members of Berger's list, and I will explain the interesting properties manifolds with holonomy G2 have and sketch the construction of examples. If time permits, I will describe some of my recent work on manifolds with closed G2-structure.<br />
<br />
===Chenxi Wu===<br />
<br />
I will discuss some of my prior works in collaboration with Harry Baik, Dongryul Kim, Hyunshik Shin and Eiko Kin on stable translation lengths on sphere graphs for maps in a fibered cone, and discuss the applications on maps on surfaces, finite graphs and handlebody groups.<br />
<br />
===Brian Hepler===<br />
<br />
We give a generalization of the notion of vanishing cycles to the setting of enhanced ind-sheaves on to any complex manifold X and holomorphic function f : X → C. Specifically, we show that there are two distinct (but Verdier-dual) functors, denoted φ+∞ and φ−∞, that deserve the name of “irregular” vanishing cycles associated to such a function f : X → C. Loosely, these functors capture the two distinct ways in which an irregular local system on the complement of the hypersurface V(f) can be extended across that hypersurface.<br />
<br />
Note: due to teaching conflict, Brian's talk will start at 2:30 in Van Vleck B313.<br />
<br />
===Botong Wang===<br />
<br />
We will give a survey of two results from combinatorics: the Heron-Rota-Welsh conjecture about the log-concavity of the coefficients of chromatic polynomials and the Top-heavy conjecture by Dowling-Wilson on the number of subspaces spanned by a finite set of vectors in a vector space. I will explain how topological and algebra-geometric methods can be relevant to such problems and how one can replace geometric arguments by combinatorial ones to extend the conclusions to non-realizable objects.<br />
<br />
===Nate Fisher===<br />
<br />
In this talk, I will define and motivate the use of horofunction boundaries in the study of groups. I will go through some examples, discuss how the horofunction boundary is related to other boundary theories, and survey a few applications of horofunction boundary.<br />
<br />
===Sigurd Angenent===<br />
<br />
Curve Shortening is the simplest and most easy to visualize of the geometric flows that have been considered in the past few decades. Nevertheless there are many open questions about the kind of singularities that can appear in CS, and several of these questions probably, hopefully, have topological answers. I'll give a short overview of what is and what isn't known. While geometric flows have had success in solving old problems in topology (Poincaré conjecture, etc.) , I would like turn things around in my talk and argue that rather than asking what analysis can do for topology, we should ask what topology can do for analysis.<br />
<br />
===Pei-Ken Hung===<br />
<br />
We establish the positive mass theorem for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity. In the umbilic case, a rigidity statement is proven showing that the total mass vanishes precisely when the initial data manifold is isometric to a portion of the canonical slice of the associated Kottler spacetime. Furthermore, we provide a new proof of the recent rigidity theorems of Eichmair-Galloway-Mendes in dimension 3, with weakened hypotheses in certain cases. These results are obtained through an analysis of the level sets of spacetime harmonic functions. This is a joint work with Aghil Alaee and Marcus Khuri.<br />
<br />
===Nianzi Li===<br />
<br />
I will introduce the definition of Higgs bundles, discuss some structures and metrics on the moduli spaces of Higgs bundles. Then I will give an overview of the results of Mazzeo-Swoboda-Weiss-Witt and Fredrickson on the exponential decay of the difference between the hyperkähler L^2 metric and the semi-flat metric along a generic ray. Finally, I will briefly talk about Boalch's modularity conjecture, and describe an ongoing work of extending the results to Higgs bundles with irregular singularities on a Riemann sphere, some of the moduli spaces are shown to be ALG gravitational instantons.<br />
<br />
== Archive of past Geometry seminars ==<br />
2020-2021 [[Geometry_and_Topology_Seminar_2020-2021]]<br />
<br><br><br />
2019-2020 [[Geometry_and_Topology_Seminar_2019-2020]]<br />
<br><br><br />
2018-2019 [[Geometry_and_Topology_Seminar_2018-2019]]<br />
<br><br><br />
2017-2018 [[Geometry_and_Topology_Seminar_2017-2018]]<br />
<br><br><br />
2016-2017 [[Geometry_and_Topology_Seminar_2016-2017]]<br />
<br><br><br />
2015-2016: [[Geometry_and_Topology_Seminar_2015-2016]]<br />
<br><br><br />
2014-2015: [[Geometry_and_Topology_Seminar_2014-2015]]<br />
<br><br><br />
2013-2014: [[Geometry_and_Topology_Seminar_2013-2014]]<br />
<br><br><br />
2012-2013: [[Geometry_and_Topology_Seminar_2012-2013]]<br />
<br><br><br />
2011-2012: [[Geometry_and_Topology_Seminar_2011-2012]]<br />
<br><br><br />
[[Fall-2010-Geometry-Topology]]<br><br />
[[Dynamics_Seminar_2020-2021]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=23012Colloquia2022-03-24T00:32:28Z<p>Amzimmer2: /* April 8, 2022, Matthew Stover (Temple University) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
'''Public Lecture: Pythagorean triples and parametrized curves'''<br />
<br />
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''<br />
<br />
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions. <br />
<br />
<br />
'''Colloquium: How irrational is an irrational variety?'''<br />
<br />
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''<br />
<br />
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.<br />
<br />
<br />
'''Seminar: Measures of association for algebraic varieties'''<br />
<br />
''Friday, March 4, 4:00pm (VV B239 )''<br />
<br />
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
'''Stochastic models of reaction networks and the Chemical Recurrence Conjecture'''<br />
<br />
Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the ''species''). <br />
<br />
If the counts of the species are low, then these systems are most often modeled as continuous-time Markov chains on $Z^d$ (with d being the number of species), with rates determined by stochastic mass-action kinetics. A natural (broad) question is: how do the qualitative properties of the dynamical system relate to the properties of the network? One specific conjecture, called the Chemical Recurrence Conjecture, and that has been open for decades, is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent (meaning the model is quite stable). <br />
<br />
I will give a general introduction to this class of models and will present the latest work towards a proof of the Chemical Recurrence Conjecture. I will make this talk accessible to graduate students, regardless of their field of study. Some of the new results presented are joint with Daniele Cappelletti, Andrea Agazzi, and Jonathan Mattingly.<br />
<br />
== March 25, 2022, Friday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom]. [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
'''Hitchin representations of Fuchsian groups'''<br />
<br />
Abstract: The Teichm&uuml;ller space $\mathcal T(S)$ of all hyperbolic structures on a fixed closed surface $S$ is a central object in geometry, topology and dynamics. It may be viewed as the orbifold universal cover of the moduli space of algebraic curves of fixed genus and also as a component of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(2,\mathbb R)$ which is topologically a cell.<br />
Hitchin discovered a component $\mathcal H_d(S)$ of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(d,\mathbb R)$<br />
which is topologically a cell. Subsequently, many striking analogies between the Hitchin component $\mathcal H_d(S)$ and Teichm&uuml;ller space $\mathcal T(S)$ were found. For example, Labourie showed that all representations in $\mathcal H_d(S)$ are discrete, faithful quasi-isometric embeddings.<br />
<br />
In this talk, we will begin by gently reviewing the parallel theories of Teichm&uuml;ller space and the Hitchin component. We will finish by reviewing a long term project to develop a geometric theory of the augmented Hitchin component which parallels the classical theory of the augmented Hitchin component (which one may view as the "orbifold universal cover" of the Deligne-Mumford compactification of Teichm&uuml;ller space). This program includes joint work with Harry Bray, Nyima Kao, Giuseppe Martone, Tengren Zhang and Andy Zimmer.<br />
<br />
== April 1, 2022, Friday at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom broadcast], [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
'''Infinite-type surfaces'''<br />
<br />
Surfaces fall into two categories: finite-type and infinite-type. The theory of infinite-type surfaces has been historically less developed than that of finite-type surfaces, but in the last few years, there has been a surge of interest in surfaces of infinite type and their mapping class groups (informally thought of as the groups of topological symmetries of these surfaces). In this talk, I will survey some of the biggest open problems in this quickly growing subfield of geometric group theory and topology, and discuss some of my own recent joint work towards resolving them.<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
'''A geometric characterization of arithmeticity'''<br />
<br />
An old, fundamental problem is classifying closed n-manifolds admitting a metric of constant curvature. The most mysterious case is constant curvature -1, that is, hyperbolic manifolds, and these divide further into "arithmetic" and "nonarithmetic" manifolds. However, it is not at all evident from the definitions that this distinction has anything to do with the differential geometry of the manifold. Uri Bader, David Fisher, Nicholas Miller and I gave a geometric characterization of arithmeticity in terms of properly immersed totally geodesic submanifolds, answering a question due independently to Alan Reid and Curtis McMullen. I will give an overview, assuming only basic differential topology, of how (non)arithmeticity and totally geodesic submanifolds are connected, then describe how this allows us to import tools from ergodic theory and homogeneous dynamics originating in groundbreaking work of Margulis to prove our characterization. Given time, I will mention some more recent developments and open questions.<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22970Colloquia2022-03-17T12:25:28Z<p>Amzimmer2: /* March 25, 2022, Friday at 4pm on Zoom. Richard Canary (Michigan) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
'''Public Lecture: Pythagorean triples and parametrized curves'''<br />
<br />
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''<br />
<br />
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions. <br />
<br />
<br />
'''Colloquium: How irrational is an irrational variety?'''<br />
<br />
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''<br />
<br />
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.<br />
<br />
<br />
'''Seminar: Measures of association for algebraic varieties'''<br />
<br />
''Friday, March 4, 4:00pm (VV B239 )''<br />
<br />
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
'''Stochastic models of reaction networks and the Chemical Recurrence Conjecture'''<br />
<br />
Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the ''species''). <br />
<br />
If the counts of the species are low, then these systems are most often modeled as continuous-time Markov chains on $Z^d$ (with d being the number of species), with rates determined by stochastic mass-action kinetics. A natural (broad) question is: how do the qualitative properties of the dynamical system relate to the properties of the network? One specific conjecture, called the Chemical Recurrence Conjecture, and that has been open for decades, is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent (meaning the model is quite stable). <br />
<br />
I will give a general introduction to this class of models and will present the latest work towards a proof of the Chemical Recurrence Conjecture. I will make this talk accessible to graduate students, regardless of their field of study. Some of the new results presented are joint with Daniele Cappelletti, Andrea Agazzi, and Jonathan Mattingly.<br />
<br />
== March 25, 2022, Friday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom]. [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
'''Hitchin representations of Fuchsian groups'''<br />
<br />
Abstract: The Teichm&uuml;ller space $\mathcal T(S)$ of all hyperbolic structures on a fixed closed surface $S$ is a central object in geometry, topology and dynamics. It may be viewed as the orbifold universal cover of the moduli space of algebraic curves of fixed genus and also as a component of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(2,\mathbb R)$ which is topologically a cell.<br />
Hitchin discovered a component $\mathcal H_d(S)$ of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(d,\mathbb R)$<br />
which is topologically a cell. Subsequently, many striking analogies between the Hitchin component $\mathcal H_d(S)$ and Teichm&uuml;ller space $\mathcal T(S)$ were found. For example, Labourie showed that all representations in $\mathcal H_d(S)$ are discrete, faithful quasi-isometric embeddings.<br />
<br />
In this talk, we will begin by gently reviewing the parallel theories of Teichm&uuml;ller space and the Hitchin component. We will finish by reviewing a long term project to develop a geometric theory of the augmented Hitchin component which parallels the classical theory of the augmented Hitchin component (which one may view as the "orbifold universal cover" of the Deligne-Mumford compactification of Teichm&uuml;ller space). This program includes joint work with Harry Bray, Nyima Kao, Giuseppe Martone, Tengren Zhang and Andy Zimmer.<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22969Colloquia2022-03-17T12:24:30Z<p>Amzimmer2: /* March 25, 2022, Friday at 4pm on Zoom. Richard Canary (Michigan) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
'''Public Lecture: Pythagorean triples and parametrized curves'''<br />
<br />
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''<br />
<br />
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions. <br />
<br />
<br />
'''Colloquium: How irrational is an irrational variety?'''<br />
<br />
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''<br />
<br />
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.<br />
<br />
<br />
'''Seminar: Measures of association for algebraic varieties'''<br />
<br />
''Friday, March 4, 4:00pm (VV B239 )''<br />
<br />
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
'''Stochastic models of reaction networks and the Chemical Recurrence Conjecture'''<br />
<br />
Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the ''species''). <br />
<br />
If the counts of the species are low, then these systems are most often modeled as continuous-time Markov chains on $Z^d$ (with d being the number of species), with rates determined by stochastic mass-action kinetics. A natural (broad) question is: how do the qualitative properties of the dynamical system relate to the properties of the network? One specific conjecture, called the Chemical Recurrence Conjecture, and that has been open for decades, is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent (meaning the model is quite stable). <br />
<br />
I will give a general introduction to this class of models and will present the latest work towards a proof of the Chemical Recurrence Conjecture. I will make this talk accessible to graduate students, regardless of their field of study. Some of the new results presented are joint with Daniele Cappelletti, Andrea Agazzi, and Jonathan Mattingly.<br />
<br />
== March 25, 2022, Friday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom]. [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
'''Hitchin representations of Fuchsian groups'''<br />
<br />
Abstract: The Teichm&uuml;ller space $\mathcal T(S)$ of all hyperbolic structures on a fixed closed surface $S$ is a central object in geometry, topology, and dynamics. It may be viewed as the orbifold universal cover of the moduli space of algebraic curves of fixed genus and also as a component of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(2,\mathbb R)$ which is topologically a cell.<br />
Hitchin discovered a component $\mathcal H_d(S)$ of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(d,\mathbb R)$<br />
which is topologically a cell. Subsequently, many striking analogies between the Hitchin component $\mathcal H_d(S)$ and Teichm&uuml;ller space $\mathcal T(S)$ were found. For example, Labourie showed that all representations in $\mathcal H_d(S)$ are discrete, faithful quasi-isometric embeddings.<br />
<br />
In this talk, we will begin by gently reviewing the parallel theories of Teichm&uuml;ller space and the Hitchin component. We will finish by reviewing a long term project to develop a geometric theory of the augmented Hitchin component which parallels the classical theory of the augmented Hitchin component (which one may view as the "orbifold universal cover" of the Deligne-Mumford compactification of Teichm&uuml;ller space). This program includes joint work with Harry Bray, Nyima Kao, Giuseppe Martone, Tengren Zhang and Andy Zimmer.<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22968Colloquia2022-03-17T12:24:10Z<p>Amzimmer2: /* March 25, 2022, Friday at 4pm on Zoom. Richard Canary (Michigan) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
'''Public Lecture: Pythagorean triples and parametrized curves'''<br />
<br />
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''<br />
<br />
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions. <br />
<br />
<br />
'''Colloquium: How irrational is an irrational variety?'''<br />
<br />
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''<br />
<br />
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.<br />
<br />
<br />
'''Seminar: Measures of association for algebraic varieties'''<br />
<br />
''Friday, March 4, 4:00pm (VV B239 )''<br />
<br />
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
'''Stochastic models of reaction networks and the Chemical Recurrence Conjecture'''<br />
<br />
Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the ''species''). <br />
<br />
If the counts of the species are low, then these systems are most often modeled as continuous-time Markov chains on $Z^d$ (with d being the number of species), with rates determined by stochastic mass-action kinetics. A natural (broad) question is: how do the qualitative properties of the dynamical system relate to the properties of the network? One specific conjecture, called the Chemical Recurrence Conjecture, and that has been open for decades, is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent (meaning the model is quite stable). <br />
<br />
I will give a general introduction to this class of models and will present the latest work towards a proof of the Chemical Recurrence Conjecture. I will make this talk accessible to graduate students, regardless of their field of study. Some of the new results presented are joint with Daniele Cappelletti, Andrea Agazzi, and Jonathan Mattingly.<br />
<br />
== March 25, 2022, Friday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom]. [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
'''Hitchin representations of Fuchsian groups'''<br />
<br />
Abstract: The Teichm&uuml;ller space $\mathcal T(S)$ of all hyperbolic structures on a fixed closed surface $S$ is a central object in geometry, topology, and dynamics. It may be viewed as the orbifold universal cover of the moduli space of algebraic curves of fixed genus and also as a component of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(2,\mathbb R)$ which is topologically a cell.<br />
Hitchin discovered a component $\mathcal H_d(S)$ of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(d,\mathbb R)$<br />
which is topologically a cell. Subsequently, many striking analogies between the Hitchin component $\mathcal H_d(S)$ and Teichm\"uller space $\mathcal T(S)$ were found. For example, Labourie showed that all representations in $\mathcal H_d(S)$ are discrete, faithful quasi-isometric embeddings.<br />
<br />
In this talk, we will begin by gently reviewing the parallel theories of Teichm&uuml;ller space and the Hitchin component. We will finish by reviewing a long term project to develop a geometric theory of the augmented Hitchin component which parallels the classical theory of the augmented Hitchin component (which one may view as the "orbifold universal cover" of the Deligne-Mumford compactification of Teichm&uuml;ller space). This program includes joint work with Harry Bray, Nyima Kao, Giuseppe Martone, Tengren Zhang and Andy Zimmer.<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22967Colloquia2022-03-17T12:23:32Z<p>Amzimmer2: /* March 25, 2022, Friday at 4pm on Zoom. Richard Canary (Michigan) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
'''Public Lecture: Pythagorean triples and parametrized curves'''<br />
<br />
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''<br />
<br />
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions. <br />
<br />
<br />
'''Colloquium: How irrational is an irrational variety?'''<br />
<br />
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''<br />
<br />
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.<br />
<br />
<br />
'''Seminar: Measures of association for algebraic varieties'''<br />
<br />
''Friday, March 4, 4:00pm (VV B239 )''<br />
<br />
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
'''Stochastic models of reaction networks and the Chemical Recurrence Conjecture'''<br />
<br />
Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the ''species''). <br />
<br />
If the counts of the species are low, then these systems are most often modeled as continuous-time Markov chains on $Z^d$ (with d being the number of species), with rates determined by stochastic mass-action kinetics. A natural (broad) question is: how do the qualitative properties of the dynamical system relate to the properties of the network? One specific conjecture, called the Chemical Recurrence Conjecture, and that has been open for decades, is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent (meaning the model is quite stable). <br />
<br />
I will give a general introduction to this class of models and will present the latest work towards a proof of the Chemical Recurrence Conjecture. I will make this talk accessible to graduate students, regardless of their field of study. Some of the new results presented are joint with Daniele Cappelletti, Andrea Agazzi, and Jonathan Mattingly.<br />
<br />
== March 25, 2022, Friday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom]. [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
'''Hitchin representations of Fuchsian groups'''<br />
<br />
Abstract: The Teichm&uuml;ller space $\mathcal T(S)$ of all hyperbolic structures on a fixed closed surface $S$ is a central object in geometry, topology, and dynamics.<br />
It may be viewed as the orbifold universal cover of the moduli space of algebraic curves of fixed genus and also as a component of<br />
the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(2,\mathbb R)$ which is topologically a cell.<br />
Hitchin discovered a component $\mathcal H_d(S)$ of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(d,\mathbb R)$<br />
which is topologically a cell. Subsequently, many striking analogies between the Hitchin component $\mathcal H_d(S)$ and Teichm\"uller space $\mathcal T(S)$ were<br />
found. For example, Labourie showed that all representations in $\mathcal H_d(S)$ are discrete, faithful quasi-isometric embeddings.<br />
<br />
In this talk, we will begin by gently reviewing the parallel theories of Teichm\"uller space and the Hitchin component. We will finish by reviewing a long<br />
term project to develop a geometric theory of the augmented Hitchin component which parallels the classical theory of the augmented Hitchin component<br />
(which one may view as the "orbifold universal cover" of the Deligne-Mumford compactification of Teichm&uuml;ller space). This program includes joint work with Harry Bray, Nyima Kao, Giuseppe Martone, Tengren Zhang and Andy Zimmer.<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22966Colloquia2022-03-17T12:19:57Z<p>Amzimmer2: /* March 25, 2022, Friday at 4pm on Zoom. Richard Canary (Michigan) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
'''Public Lecture: Pythagorean triples and parametrized curves'''<br />
<br />
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''<br />
<br />
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions. <br />
<br />
<br />
'''Colloquium: How irrational is an irrational variety?'''<br />
<br />
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''<br />
<br />
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.<br />
<br />
<br />
'''Seminar: Measures of association for algebraic varieties'''<br />
<br />
''Friday, March 4, 4:00pm (VV B239 )''<br />
<br />
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
'''Stochastic models of reaction networks and the Chemical Recurrence Conjecture'''<br />
<br />
Cellular, chemical, and population processes are all often represented via networks that describe the interactions between the different population types (typically called the ''species''). <br />
<br />
If the counts of the species are low, then these systems are most often modeled as continuous-time Markov chains on $Z^d$ (with d being the number of species), with rates determined by stochastic mass-action kinetics. A natural (broad) question is: how do the qualitative properties of the dynamical system relate to the properties of the network? One specific conjecture, called the Chemical Recurrence Conjecture, and that has been open for decades, is the following: if each connected component of the network is strongly connected, then the associated stochastic model is positive recurrent (meaning the model is quite stable). <br />
<br />
I will give a general introduction to this class of models and will present the latest work towards a proof of the Chemical Recurrence Conjecture. I will make this talk accessible to graduate students, regardless of their field of study. Some of the new results presented are joint with Daniele Cappelletti, Andrea Agazzi, and Jonathan Mattingly.<br />
<br />
== March 25, 2022, Friday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom]. [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
'''Hitchin representations of Fuchsian groups'''<br />
<br />
Abstract: The Teichmuller space $\mathcal T(S)$ of all hyperbolic structures on a fixed closed surface $S$ is a central object in geometry, topology, and dynamics.<br />
It may be viewed as the orbifold universal cover of the moduli space of algebraic curves of fixed genus and also as a component of<br />
the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(2,\mathbb R)$ which is topologically a cell.<br />
Hitchin discovered a component $\mathcal H_d(S)$ of the space of (conjugacy classes of) representations of $\pi_1(S)$ into $\mathsf{PSL}(d,\mathbb R)$<br />
which is topologically a cell. Subsequently, many striking analogies between the Hitchin component $\mathcal H_d(S)$ and Teichm\"uller space $\mathcal T(S)$ were<br />
found. For example, Labourie showed that all representations in $\mathcal H_d(S)$ are discrete, faithful quasi-isometric embeddings.<br />
<br />
In this talk, we will begin by gently reviewing the parallel theories of Teichm\"uller space and the Hitchin component. We will finish by reviewing a long<br />
term project to develop a geometric theory of the augmented Hitchin component which parallels the classical theory of the augmented Hitchin component<br />
(which one may view as the "orbifold universal cover" of the Deligne-Mumford compactification of Teichm\"uller space). This program includes joint work with Harry Bray, Nyima Kao, Giuseppe Martone, Tengren Zhang and Andy Zimmer.<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22902Colloquia2022-03-01T19:56:56Z<p>Amzimmer2: /* March 25, 2022, Friday at 4pm on Zoom Richard Canary (Michigan) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
'''Public Lecture: Pythagorean triples and parametrized curves'''<br />
<br />
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''<br />
<br />
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions. <br />
<br />
<br />
'''Colloquium: How irrational is an irrational variety?'''<br />
<br />
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''<br />
<br />
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.<br />
<br />
<br />
'''Seminar: Measures of association for algebraic varieties'''<br />
<br />
''Friday, March 4, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream])''<br />
<br />
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
(local)<br />
<br />
== March 25, 2022, Friday at 4pm on Zoom. [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 22, 2022, [https://www.math.uni-kiel.de/analysis/de/mueller Detlef Müller] (Kiel, Germany) ==<br />
<br />
(hosted by Seeger and Stovall)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22901Colloquia2022-03-01T19:56:44Z<p>Amzimmer2: /* March 25, 2022, Richard Canary (Michigan) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live Stream], [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 1, 2 and 4, 2022 (Tuesday, Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
'''Public Lecture: Pythagorean triples and parametrized curves'''<br />
<br />
''Tuesday, March 1, 4:00pm (Humanities 3650 + [http://go.wisc.edu/n6986j Live Stream]). Note unusual time and location!''<br />
<br />
In this lecture, aimed at advanced undergraduate and beginning graduate students, I will discuss the question of when a curve in the plane admits a parameterization by polynomials or rational functions. <br />
<br />
<br />
'''Colloquium: How irrational is an irrational variety?'''<br />
<br />
''Wednesday, March 2, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream]).''<br />
<br />
Recall that an algebraic variety is said to be rational if it has a Zariski open subset that is isomorphic to an open subset of projective space. There has been a great deal of recent activity and progress on questions of rationality, but most varieties aren't rational. I will survey a body of work concerned with measuring and controlling “how irrational” a given variety might be.<br />
<br />
<br />
'''Seminar: Measures of association for algebraic varieties'''<br />
<br />
''Friday, March 4, 4:00pm (VV B239 + [http://go.wisc.edu/wuas48 Live Stream])''<br />
<br />
I will discuss some recent work with Olivier Martin that attempts to quantify how far two varieties are from being birationally isomorphic. Besides presenting a few results, I will discuss many open problems and avenues for further investigation.<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
(local)<br />
<br />
== March 25, 2022, Friday at 4pm on Zoom [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 22, 2022, [https://www.math.uni-kiel.de/analysis/de/mueller Detlef Müller] (Kiel, Germany) ==<br />
<br />
(hosted by Seeger and Stovall)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia/Fall2022&diff=22900Colloquia/Fall20222022-03-01T19:49:21Z<p>Amzimmer2: Created page with "== September 30, 2022, Friday at 4pm [https://math.wisc.edu TBA] (TBA) == (host: Guo, Seeger)"</p>
<hr />
<div>== September 30, 2022, Friday at 4pm [https://math.wisc.edu TBA] (TBA) ==<br />
<br />
(host: Guo, Seeger)</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22787Colloquia2022-02-18T18:50:17Z<p>Amzimmer2: /* February 25, 2022, Rohini Ramadas (Warwick) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
'''Dynamics on the moduli space of point-configurations on the Riemann sphere'''<br />
<br />
A degree-$d$ rational function $f(z)$ in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space $M_{0,n}$ of point-configurations on the Riemann sphere. I will introduce PCF maps and $M_{0,n}$. I will then present results characterizing the ensuing dynamics on $M_{0,n}$. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 2 and 4, 2022 (Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
(local)<br />
<br />
== March 25, 2022, [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 22, 2022, [https://www.math.uni-kiel.de/analysis/de/mueller Detlef Müller] (Kiel, Germany) ==<br />
<br />
(hosted by Seeger and Stovall)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22786Colloquia2022-02-18T18:49:35Z<p>Amzimmer2: /* February 25, 2022, Rohini Ramadas (Warwick) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, at 4pm in B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Video over Zoom], [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
Dynamics on the moduli space of point-configurations on the Riemann sphere<br />
<br />
A degree-d rational function f(z) in one variable with complex coefficients defines a holomorphic self-map of the Riemann sphere. A rational function is called post-critically finite (PCF) if every critical point is (pre)-periodic. PCF rational functions have been central in complex dynamics, due to their special dynamical behavior, and their special distribution within the parameter space of all rational maps. <br />
<br />
By work of Koch building on a result of Thurston, every PCF map arises as an isolated fixed point of an algebraic dynamical system on the moduli space M_{0,n} of point-configurations on the Riemann sphere. I will introduce PCF maps and M_{0,n}. I will then present results characterizing the ensuing dynamics on M_{0,n}. <br />
<br />
This talk includes joint work with Nguyen-Bac Dang, Sarah Koch, David Speyer, and Rob Silversmith.<br />
<br />
== March 2 and 4, 2022 (Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
(local)<br />
<br />
== March 25, 2022, [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 22, 2022, [https://www.math.uni-kiel.de/analysis/de/mueller Detlef Müller] (Kiel, Germany) ==<br />
<br />
(hosted by Seeger and Stovall)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
(''Departmental Distinguished Lecture series'')<br />
<br />
== May 10+12, 2022, Tuesday+Thursday, 12pm on Zoom. [http://www.ma.huji.ac.il/~kalai/ Gil Kalai] (Hebrew University) ==<br />
<br />
(''Hilldale Lectures / Special colloquium'')<br />
<br />
'''The argument against quantum computers'''<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22669Colloquia2022-02-06T15:33:32Z<p>Amzimmer2: /* February 11, 2022, Mariya Soskova (UW-Madison) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
'''The e-verse'''<br />
<br />
Computability theory studies the relative algorithmic complexity of sets of natural numbers and other mathematical objects. Turing reducibility and the induced partial order of the Turing degrees serve as the well-established model of relative computability. Enumeration reducibility captures another natural relationship between sets of natural numbers in which positive information about the first set is used to produce positive information about the second set. The induced structure of the enumeration degrees can be viewed as an extension of the Turing degrees, as there is a natural way to embed the second partial order in the first. In certain cases, the enumeration degrees can be used to capture the algorithmic content of mathematical objects, while the Turing degrees fail. Certain open problems in degree theory present as more approachable in the extended context of the enumeration degrees, e.g. first order definability. We have been working to develop a richer “e-verse”: a system of classes of enumeration degrees with interesting properties and relationships, in order to better understand the enumeration degrees. I will outline several research directions in this context.<br />
<br />
== February 18, 2022, [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
== March 2 and 4, 2022 (Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
<br />
('''Departmental Distinguished Lecture series''')<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
(local)<br />
<br />
== March 25, 2022, [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 22, 2022, [https://www.math.uni-kiel.de/analysis/de/mueller Detlef Müller] (Kiel, Germany) ==<br />
<br />
(hosted by Seeger and Stovall)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
('''Departmental Distinguished Lecture series''')<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22658Colloquia2022-02-04T16:35:17Z<p>Amzimmer2: /* February 18, 2022, Andreas Seeger (UW-Madison) */</p>
<hr />
<div>__NOTOC__<br />
<br />
<br />
<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
<br />
<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
<br />
<br />
== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Surface phenomena in the 2D and 3D Ising model'''<br />
<br />
Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
<br />
== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Symmetries of surfaces: big and small'''<br />
<br />
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
<br />
== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
<br />
In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
<br />
== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
<br />
'''From simple groups to symmetries of surfaces'''<br />
<br />
We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
<br />
== February 11, 2022, [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
<br />
(local)<br />
<br />
== February 18, 2022, [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
<br />
'''Spherical maximal functions and fractal dimensions of dilation sets'''<br />
<br />
We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
<br />
== February 25, 2022, [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
<br />
(hosted by WIMAW)<br />
<br />
== March 2 and 4, 2022 (Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
<br />
('''Departmental Distinguished Lecture series''')<br />
<br />
== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
<br />
(local)<br />
<br />
== March 25, 2022, [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
<br />
(hosted by WIMAW)<br />
<br />
== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
<br />
== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
<br />
(hosted by Gong)<br />
<br />
== April 22, 2022, [https://www.math.uni-kiel.de/analysis/de/mueller Detlef Müller] (Kiel, Germany) ==<br />
<br />
(hosted by Seeger and Stovall)<br />
<br />
== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
<br />
('''Departmental Distinguished Lecture series''')<br />
<br />
== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
<br />
== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
<br />
[[Colloquia/Spring2016|Spring 2016]]<br />
<br />
[[Colloquia/Fall2015|Fall 2015]]<br />
<br />
[[Colloquia/Spring2014|Spring 2015]]<br />
<br />
[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
<br />
[[WIMAW]]</div>Amzimmer2https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22657Colloquia2022-02-04T16:34:54Z<p>Amzimmer2: /* February 18, 2022, Andreas Seeger (UW-Madison) */</p>
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<div>__NOTOC__<br />
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<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b><br />
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<!--- in Van Vleck B239, '''unless otherwise indicated'''. ---><br />
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== January 10, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://www.stat.berkeley.edu/~gheissari/ Reza Gheissari] (UC Berkeley) ==<br />
<br />
(reserved by the hiring committee)<br />
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'''Surface phenomena in the 2D and 3D Ising model'''<br />
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Since its introduction in 1920, the Ising model has been one of the most studied models of phase transitions in statistical physics. In its low-temperature regime, the model has two thermodynamically stable phases, which, when in contact with each other, form an interface: a random curve in 2D and a random surface in 3D. In this talk, I will survey the rich phenomenology of this interface in 2D and 3D, and describe recent progress in understanding its geometry in various parameter regimes where different surface phenomena and universality classes emerge.<br />
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== January 17, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/lovingmath/home Marissa Loving] (Georgia Tech) ==<br />
<br />
(reserved by the hiring committee)<br />
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'''Symmetries of surfaces: big and small'''<br />
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We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played a central role in low-dimensional topology stretching back a hundred years to work of Max Dehn and Jakob Nielsen, and gaining momentum and significance through the celebrated work of Bill Thurston on the geometry of 3-manifolds. In comparison, the study of the mapping class group of infinite-type surfaces has exploded only within the past few years. Nevertheless, infinite-type surfaces appear quite regularly in the wilds of mathematics with connections to dynamics, the topology of 3-manifolds, and even descriptive set theory -- there is a great deal of rich mathematics to be gained in their study! In this talk, we will discuss the way that the study of surfaces intersects and interacts with geometry, algebra, and number theory, as well as some of my own contributions to this vibrant area of study.<br />
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== January 21, 2022, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://web.math.princeton.edu/~nfm2/ Nicholas Marshall] (Princeton) ==<br />
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(reserved by the hiring committee)<br />
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'''Laplacian quadratic forms, function regularity, graphs, and optimal transport'''<br />
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In this talk, I will discuss two different applications of harmonic analysis to<br />
problems motivated by data science. Both problems involve using Laplacian<br />
quadratic forms to measure the regularity of functions. In both cases the key<br />
idea is to understand how to modify these quadratic forms to achieve a specific<br />
goal. First, in the graph setting, we suppose that a collection of m graphs<br />
G_1 = (V,E_1),...,G_m=(V,E_m) on a common set of vertices V is given,<br />
and consider the problem of finding the 'smoothest' function f : V -> R with<br />
respect to all graphs simultaneously, where the notion of smoothness is defined<br />
using graph Laplacian quadratic forms. Second, on the unit square [0,1]^2, we<br />
consider the problem of efficiently computing linearizations of 2-Wasserstein<br />
distance; here, the solution involves quadratic forms of a Witten Laplacian.<br />
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== January 24, 2022, Monday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream] + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Chat over Zoom], [https://sites.google.com/view/skippermath Rachel Skipper] (Ohio State) ==<br />
<br />
(reserved by the hiring committee)<br />
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'''From simple groups to symmetries of surfaces'''<br />
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We will take a tour through some families of groups of historic importance in geometric group theory, including self-similar groups and Thompson’s groups. We will discuss the rich, continually developing theory of these groups which act as symmetries of the Cantor space, and how they can be used to understand the variety of infinite simple groups. Finally, we will discuss how these groups are serving an important role in the newly developing field of big mapping class groups which are used to describe symmetries of surfaces.<br />
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== February 11, 2022, [https://people.math.wisc.edu/~msoskova/ Mariya Soskova] (UW-Madison) ==<br />
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(local)<br />
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== February 18, 2022, [https://people.math.wisc.edu/~seeger/ Andreas Seeger] (UW-Madison) ==<br />
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"Spherical maximal functions and fractal dimensions of dilation sets"<br />
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We survey old and new problems and results on spherical means, regarding pointwise convergence, $L^p$ improving and consequences for sparse domination.<br />
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== February 25, 2022, [https://sites.google.com/view/rohini-ramadas/home Rohini Ramadas] (Warwick) == <br />
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(hosted by WIMAW)<br />
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== March 2 and 4, 2022 (Wednesday and Friday), [http://www.math.stonybrook.edu/~roblaz/ Robert Lazarsfeld] (Stony Brook) ==<br />
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('''Departmental Distinguished Lecture series''')<br />
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== March 11, 2022, [https://people.math.wisc.edu/~anderson/ David Anderson] (UW-Madison) ==<br />
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(local)<br />
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== March 25, 2022, [http://www.math.lsa.umich.edu/~canary/ Richard Canary] (Michigan) ==<br />
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(hosted by Zimmer)<br />
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== April 1, 2022, [https://www.patelp.com/ Priyam Patel] (Utah) ==<br />
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(hosted by WIMAW)<br />
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== April 8, 2022, [https://math.temple.edu/~tuf27009/index.html Matthew Stover] (Temple University) ==<br />
<br />
(hosted by Zimmer)<br />
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== April 15, 2022, [https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel Bernhard Lamel], (Texas A&M University at Qatar) ==<br />
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(hosted by Gong)<br />
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== April 22, 2022, [https://www.math.uni-kiel.de/analysis/de/mueller Detlef Müller] (Kiel, Germany) ==<br />
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(hosted by Seeger and Stovall)<br />
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== April 25-26-27 (Monday [VV B239], Tuesday [Chamberlin 2241], Wednesday [VV B239]) 4 pm [https://math.mit.edu/directory/profile.php?pid=1461 Larry Guth] (MIT) ==<br />
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('''Departmental Distinguished Lecture series''')<br />
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== Future Colloquia ==<br />
<br />
[[Colloquia/Fall2022|Fall 2022]]<br />
<br />
[[Colloquia/Spring2023|Spring 2023]]<br />
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== Past Colloquia ==<br />
[[Colloquia/Fall2021|Fall 2021]]<br />
<br />
[[Colloquia/Spring2021|Spring 2021]]<br />
<br />
[[Colloquia/Fall2020|Fall 2020]]<br />
<br />
[[Colloquia/Spring2020|Spring 2020]]<br />
<br />
[[Colloquia/Fall2019|Fall 2019]]<br />
<br />
[[Colloquia/Spring2019|Spring 2019]]<br />
<br />
[[Colloquia/Fall2018|Fall 2018]]<br />
<br />
[[Colloquia/Spring2018|Spring 2018]]<br />
<br />
[[Colloquia/Fall2017|Fall 2017]]<br />
<br />
[[Colloquia/Spring2017|Spring 2017]]<br />
<br />
[[Archived Fall 2016 Colloquia|Fall 2016]]<br />
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[[Colloquia/Spring2016|Spring 2016]]<br />
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[[Colloquia/Fall2015|Fall 2015]]<br />
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[[Colloquia/Spring2014|Spring 2015]]<br />
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[[Colloquia/Fall2014|Fall 2014]]<br />
<br />
[[Colloquia/Spring2014|Spring 2014]]<br />
<br />
[[Colloquia/Fall2013|Fall 2013]]<br />
<br />
[[Colloquia 2012-2013|Spring 2013]]<br />
<br />
[[Colloquia 2012-2013#Fall 2012|Fall 2012]]<br />
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[[WIMAW]]</div>Amzimmer2