Geometry and Topology Seminar 2019-2020: Difference between revisions

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== Spring 2013 ==
 
== Fall 2013==
 
 
 
{| cellpadding="8"
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!align="left" | speaker
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|September 21
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|September 28
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|October 5
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|October 12
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|October 19
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|October 26
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|November 2
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|November 9
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|November 16
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| Thanksgiving Recess
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|November 30
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|December 7
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== Fall Abstracts ==
 
== Spring 2014 ==




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|January 25
|January 25
| [http://www.maths.usyd.edu.au/u/athomas/ Anne Thomas] (Sydney)
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| [[#Anne Thomas (Sydney)| ''Divergence in right-angled Coxeter groups'']]
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|[http://www.math.wisc.edu/~dymarz/ Dymarz]
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|February 1
|February 1
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|February 15
|February 15
| [http://www3.nd.edu/~lnicolae/ Liviu Nicolaescu] (Notre Dame)
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| [[#Liviu Nicolaescu (Notre Dame)| ''Random Morse functions and spectral geometry'']]
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|[http://www.math.wisc.edu/~oh/ Oh]
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|February 22
|February 22
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|March 1
|March 1
| [https://pantherfile.uwm.edu/chruska/www/ Chris Hruska] (UW Milwaukee)
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| [[#Chris Hruska (UW Milwaukee)| ''Local topology of boundaries and isolated flats'']]
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|[http://www.math.wisc.edu/~dymarz/ Dymarz]
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|March 8
|March 8
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|March 11, <b>MONDAY in B113!</b>
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| [http://www.math.fsu.edu/~hironaka/ Eriko Hironaka] (FSU)
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| [[#Eriko Hironaka (FSU)| ''Small dilatation pseudo-Anosov mapping classes'']]
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|[http://www.math.wisc.edu/~rkent/ Kent]
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|March 15
|March 15
| Yu-Shen Lin (Harvard)
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| [[#Yu-Shen Lin (Harvard)| ''Open Gromov-Witten Invariants on K3 surfaces and Wall-Crossing'']]
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| [http://www.math.wisc.edu/~oh/ Oh]
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|March 20 <b>WEDNESDAY in 901!</b>
|  
|[http://www.math.nyu.edu/faculty/cappell/index.html Sylvain Cappell] (NYU)
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|[[#Sylvain Cappell (NYU)| ''Topological actions of compact, connected Lie Groups on Manifolds'']]
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| [http://www.math.wisc.edu/~maxim/ Maxim]
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|Spring Break
|Spring Break
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|April 12
|  
|[http://www.mathi.uni-heidelberg.de/~villa/ Manuel Gonzalez Villa] (Heidelberg)
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|[[#Manuel Gonzalez Villa (Heidelberg)| '' The monodromy conjecture for plane meromorphic germs'']]
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|Maxim
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|April 19
|April 19
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|April 26
|April 26
| Emmy Murphy (MIT)
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| [[#Emmy Murphy (MIT) | ''Exact Lagrangian immersions with few transverse self intersections'']]
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| [http://www.math.wisc.edu/~oh/ Oh]
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|May 3
|May 3
| Yuan-qi Wang (UCSB)
|  
| [[#Yuan-qi Wang (UCSB)| ''Bessel Functions, Heat Kernel and the Conical Kahler-Ricci 
|
Flow'']]
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| [http://www.math.wisc.edu/~bwang/ Wang]
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|May 10
|May 10
| [http://www.math.wisc.edu/~oh/ Yong-Geun Oh] (Wisconsin)
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| [[#Yong-Geun Oh (Wisconsin)| ''Analysis of contact instantons and contact homology'']]
| Local
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|}
 
== Spring Abstracts ==
 
===Anne Thomas (Sydney)===
''Divergence in right-angled Coxeter groups''
 
Abstract:
The divergence of a pair of geodesic rays emanating from a point is a
measure of how quickly they are moving away from each other. In
Euclidean space divergence is linear, while in hyperbolic space
divergence is exponential. Gersten used this idea to define a
quasi-isometry invariant for groups, also called divergence, which has
been investigated for classes of groups including fundamental groups
of 3-manifolds, mapping class groups and right-angled Artin groups. I
will discuss joint work with Pallavi Dani on divergence in
right-angled Coxeter groups (RACGs).  We characterise 2-dimensional
RACGs with quadratic divergence, and prove that for every positive
integer d, there is a RACG with divergence polynomial of degree d.
 
===Liviu Nicolaescu (Notre Dame)===
''Random Morse functions and spectral geometry''
 
Abstract:
I will discuss the distribution of critical values of a  smooth random function on a compact m-dimensional Riemann manifold (M,g)  described as a random  superposition  of eigenfunctions of the Laplacian.  The  notion of randomness that we use    has a naturally  built in  small parameter $\varepsilon$, and we show that    as $\varepsilon\to 0$ the distribution of critical  values closely resemble the distribution  of eigenvalues  of  certain  random symmetric  $(m+1)\times (m+1)$-matrices  of the type introduced by E. Wigner  in quantum mechanics. Additionally, I will  explain how to recover the metric  $g$ from  statistical  properties of the Hessians of the above random function.
 
===Chris Hruska (UW Milwaukee)===
''Local topology of boundaries and isolated flats''
 
Abstract:  Swarup proved that every one-ended word hyperbolic group has a
locally connected Gromov boundary.  However for CAT(0) groups,
non-locally connected boundaries are easy to construct.  For instance
the boundary of F_2 x Z is the suspension of a Cantor set.
 
In joint work with Kim Ruane, we have studied boundaries of CAT(0)
spaces with isolated flats.  If G acts properly, cocompactly on such a
space X, we give a necessary and sufficient condition on G such that
the boundary of X is locally connected.  As a corollary, we deduce
that such a group G is semistable at infinity.
 
===Eriko Hironaka (FSU)===
''Small dilatation pseudo-Anosov mapping classes''
 
The theory of fibered faces implies that  pseudo-Anosov
mapping classes with bounded normalized dilatation can be partitioned
into a finite number of families with related dynamics.  In this talk we
discuss the problem of finding concrete description
of the members of these families.  One conjectural way generalizes a
well-known sequence
defined by Penner in '91.  However, so far no known examples  of
this type come close to
the smallest known accumulation point of normalized dilatations.
In this talk we describe a different construction that uses mixed-sign
Coxeter systems.  A deformation of the simplest pseudo-Anosov braid monodromy
can be obtained in this way, and hence this model does realize the
smallest known accumulation point.
 
===Yu-Shen Lin (Harvard)===
''Open Gromov-Witten Invariants on K3 surfaces and Wall-Crossing''
 
Strominger-Yau-Zaslow conjecture suggests that the Ricci-flat metric on Calabi-Yau manifolds might be related to holomorphic discs. In this talk, I will define a new open Gromov-Witten invariants on elliptic K3 surfaces trying to explain this conjecture. The new invariant satisfies certain wall-crossing formula and multiple cover formula. I will also establish a tropical-holomorphic correspondence. Moreover, this invariant is expected to be equivalent to the generalized Donaldson-Thomas invariants in the hyperK\"ahler metric constructed by Gaiotto-Moore-Neitzke. If time allowed, I will talk about the connection with disks counting on Calabi-Yau 3-folds.
 
===Sylvain Cappell (NYU)===
''TBA''
 
===Manuel Gonzalez Villa (Heidelberg)===
''The monodromy conjecture for plane meromorphic germs''
 
Joint work with  Ann Lemahieu (Lille). A notion of Milnor fibration  for meromorphic functions and the corresponding concepts of  monodromy and monodromy zeta function, introduced by Gussein-Zade, Luengo and Melle, invite to consider the notion of  topological zeta function for meromorphic germs and the corresponding monodromy conjecture. We try to motive these notions and discuss the plane case. We show that the poles do not behave as in the holomorphic case but still do satisfy a generalization of the monodromy conjecture.
 
===Emmy Murphy (MIT)===
''Exact Lagrangian immersions with few transverse self intersections''
 
This talk will focus on the following question: supposing a
smooth manifold immerses into C^n as an exact Lagrangian, what is the
minimal number of transverse self-intersections necessary? Finding lower
bounds on the number of intersections of two embedded Lagrangians is a
central problem in symplectic topology which has seen much success; in
contrast bounding the number of self-intersections of an exact Lagrangian
immersion requires more advanced tools and the known results are far less
general. We show that no Arnold-type lower bound exists for exact
Lagrangian immersions by constructing examples with surprisingly few
self-intersections. For example, we show that any three-manifold immerses
as an exact Lagrangian in C^3 with a single transverse self-intersection.
We also apply Lagrangian surgery to these immersions to give some
interesting new examples of Lagrangian embeddings. (This is joint work of
the speaker with T. Ekholm, Y. Eliashberg, and I. Smith.)
 
===Yuan-qi Wang (UCSB)===
''Bessel Functions, Heat Kernel and the Conical Kahler-Ricci 
Flow''
 
Inspired by Donaldson's program, we introduce the Kahler 
Ricci flow with conical singularities. The main part of this talk is 
to show that the conical Kahler Ricci flow exists for short time and 
for long time in a proper space. These existence results are highly 
related to heat kernel and Bessel functions. We will also discuss some 
easy applications of the conical Kahler Ricci flow in conical Kahler 
geometry.
 
===Yong-Geun Oh (Wisconsin)===
''Analysis of contact instantons and contact homology''
 
In this talk, we explain the analysis of the following system of (degenerate) elliptic equation
$$
\overline \partial^\pi w = 0, \, d(w^*\lambda \circ j) = 0
$$
associated for each given contact triad $(Q,\lambda,J)$ on a contact manifold $(Q,\xi)$.
(Such an equation was first introduced by Hofer.)  We directly work with this equation
on the contact manifold without involving the symplectization process. We explain the basic
analytical ingredients towards the construction of moduli space of
solutions, which we call contact instantons.  I will indicate how one can define contact
homology type invariants using such a moduli space, which is still in progress. The talk
is partially based on the joint work with Rui Wang.
 
 
== Fall 2012==
 
 
 
{| cellpadding="8"
!align="left" | date
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
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|September 21
| [http://www.math.wisc.edu/~josizemore/ Owen Sizemore] (Wisconsin)
| [[#Owen Sizemore (Wisconsin) |
''Operator Algebra Techniques in Measureable Group Theory'']]
| local
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|September 28
|[https://engineering.purdue.edu/~mboutin/ Mireille Boutin] (Purdue)
|[[#Mireille Boutin (Purdue) |
''The Pascal Triangle of a discrete Image: <br>
definition, properties, and application to object segmentation'']]
|[http://www.math.wisc.edu/~maribeff/ Mari Beffa]
|-
|October 5
| [http://www.math.msu.edu/~schmidt/ Ben Schmidt] (Michigan State)
| [[#Ben Schmidt (Michigan State)|
''Three manifolds of constant vector curvature'']]
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
|-
|October 12
| [https://www2.bc.edu/ian-p-biringer/ Ian Biringer] (Boston College)
| [[#Ian Biringer (Boston College)|
''Growth of Betti numbers and a probabilistic take on Gromov Hausdorff convergence'']]
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
|-
|October 19
| Peng Gao (Simons Center for Geometry and Physics)
| [[#Peng Gao (Simons Center for Geometry and Physics)|
''string theory partition functions and geodesic spectrum'']]
|[http://www.math.wisc.edu/~bwang/ Wang]
|-
|October 26
| [http://www.math.wisc.edu/~nelson/ Jo Nelson] (Wisconsin)
| [[#Jo Nelson (Wisconsin) |
''Cylindrical contact homology as a well-defined homology theory? Part I'']]
| local
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|November 2
| [http://www.bowdoin.edu/~jtaback/ Jennifer Taback] (Bowdoin)
| [[#Jennifer Taback (Bowdoin)|
''The geometry of twisted conjugacy classes in Diestel-Leader groups'']]
|[http://www.math.wisc.edu/~dymarz/ Dymarz]
|-
|November 9
| [http://math.uchicago.edu/~wilsonj/ Jenny Wilson] (Chicago)
| [[#Jenny Wilson (Chicago)|
''FI-modules for Weyl groups'']]
| [http://www.math.wisc.edu/~ellenber/ Ellenberg]
|-
|November 16
|[http://www.math.uic.edu/people/profile?id=GasJ574 Jonah Gaster] (UIC)
|[[#Jonah Gaster (UIC)|
''A Non-Injective Skinning Map with a Critical Point'']]
|[http://www.math.wisc.edu/~rkent/ Kent]
|-
| Thanksgiving Recess
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|November 30
| [http://www.its.caltech.edu/~shinpei/ Shinpei Baba] (Caltech)
|[[#Shinpei Baba (Caltech)|
''Grafting and complex projective structures'']]
|[http://www.math.wisc.edu/~rkent/ Kent]
|-
|-
|December 7
| [http://math.uchicago.edu/~mann/ Kathryn Mann] (Chicago)
|[[#Kathryn Mann (Chicago)|
''The group structure of diffeomorphism groups'']]
|[http://www.math.wisc.edu/~rkent/ Kent]
|-
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|}
|}


== Fall Abstracts ==
== Spring Abstracts ==
 
===Owen Sizemore (Wisconsin)===
''Operator Algebra Techniques in Measureable Group Theory''
 
Measurable group theory is the study of groups via their actions on measure spaces. While the classification for amenable groups was essentially complete by the early 1980's,  progress for nonamenable groups has been slow to emerge. The last 15 years has seen a surge in the classification of ergodic actions of nonamenable groups, with methods coming from diverse areas. We will survey these new results, as well as, give an introduction to the operator algebra techniques that have been used.
 
===Mireille Boutin (Purdue)===
''The Pascal Triangle of a discrete Image: definition, properties, and application to object segmentation''
 
We define the Pascal Triangle of a discrete (gray scale) image as a pyramidal ar-
rangement of complex-valued moments and we explore its geometric significance. In
particular, we show that the entries of row k of this triangle correspond to the Fourier
series coefficients of the moment of order k of the Radon transform of the image. Group
actions on the plane can be naturally prolonged onto the entries of the Pascal Triangle. We study the induced action of some common group actions, such as translation,
rotations, and reflections, and we propose simple tests for equivalence and self-
equivalence for these group actions. The motivating application of this work is the
problem of recognizing ”shapes” on images, for example characters, digits or simple
graphics. Application to the MERGE project, in which we developed a fast method for segmenting hazardous material signs on a cellular phone, will be also discussed.
 
This is joint work with my graduate students Shanshan Huang and Andrew Haddad.
 
===Ben Schmidt (Michigan State)===
''Three manifolds of constant vector curvature.''
 
A Riemannian manifold M is said to have extremal curvature K if all sectional curvatures are bounded above by K or if all sectional curvatures are bounded below by K.  A manifold with extremal curvature K has constant vector curvature K if every tangent vector to M belongs to a tangent plane of curvature K.  For surfaces, having constant vector curvature is equivalent to having constant curvature.  In dimension three, the eight Thurston geometries all have constant vector curvature.  In this talk, I will discuss the classification of closed three manifolds with constant vector curvature.  Based on joint work with Jon Wolfson.
 
===Ian Biringer (Boston College)===
''Growth of Betti numbers and a probabilistic take on Gromov Hausdorff convergence''
 
We will describe an asymptotic relationship between the volume and the Betti numbers of certain locally symmetric spaces. The proof uses an exciting new tool: a synthesis of Gromov-Hausdorff convergence of Riemannian manifolds and Benjamini-Schramm convergence from graph theory.
 
===Peng Gao (Simons Center for Geometry and Physics)===
''string theory partition functions and geodesic spectrum''
 
String theory partition functions often have nice modular properties, which is well understood within the context of representation theory of (supersymmetric extensions) of Virasoro algebra.
However, many questions of physical importance are preferrably addressed when string theory is formulated in terms of non-linear sigma model on a Riemann surface with a Riemannian manifold as target space. Traditionally, physicists have studied such sigma models within the realm of perturbation theory, overlooking a large class of very natural critical points of the path integral, namely, closed geodesics on the target space Riemannian manifold. We propose how to take into account the effect of these critical points on the path integral, and initiate its study on Ricci flat targe spaces, such as the K3 surface.
 
===Jo Nelson (Wisconsin)===
''Cylindrical contact homology as a well-defined homology theory? Part I''
 
In this talk I will define all the concepts in the title, starting with what a contact manifold is.  I will also  explain how the heuristic arguments sketched in the literature since 1999 fail to define a homology theory and provide a foundation for a well-defined cylindrical contact homology, while still providing an invariant of the contact structure.  A later talk will provide us with a large class of examples under which one can compute a well-defined version of cylindrical contact homology via a new approach the speaker developed for her thesis that is distinct and completely independent of previous specialized attempts.
 
===Jennifer Taback (Bowdoin)===
''The geometry of twisted conjugacy classes in Diestel-Leader groups''
 
The problem of computing the Reidemsieter number R(f)  of a group automorphism f, that is, the number of f-twisted conjugacy classes, is related to questions in Lefschetz-Nielsen fixed point theory.  We say a group has property R-infinity if every group automorphism has infinitely many twisted conjugacy classes.  This property has been studied by Fel’shtyn, Gonzalves, Wong, Lustig, Levitt and others, and has applications outside of topology.
Twisted conjugacy classes in lamplighter groups are well understood both geometrically and algebraically.  In particular the lamplighter group L_n does not have property R-infinity iff (n,6)=1. In this talk I will extend these results to Diestel-Leader groups with a surprisingly different conclusion.  The family of Diestel-Leader groups provides a natural geometric generalization of the lamplighter groups.  I will define these groups, as well as Diestel-Leader graphs and describe how these results include a computation of the automorphism group of this family.
This is joint work with Melanie Stein and Peter Wong.
 
===Jenny Wilson (Chicago)===
''FI-modules for Weyl groups''
 
Earlier this year, Church, Ellenberg, and Farb developed a new framework for studying sequences of representations of the symmetric groups, using a concept they call an FI--module. I will give an overview of this theory, and describe how it generalizes to sequences of representations of the classical Weyl groups in Type B/C and D. The theory of FI--modules has provided a wealth of new results by numerous authors working in algebra, geometry, and topology. I will outline some of these results, including applications to configurations spaces and groups related to the braid group.
 
===Jonah Gaster (UIC)===
''A Non-Injective Skinning Map with a Critical Point''
 
Following Thurston, certain classes of 3-manifolds yield holomorphic maps on the Teichmuller spaces of their boundary components. Inspired by numerical evidence of Kent and Dumas, we present a negative result about the regularity of such maps. Namely, we construct a path of deformations of the hyperbolic structure on a genus-2 handlebody, with two rank-1 cusps. The presence of some extra symmetry yields information about the convex core, which is used to conclude some inequalities involving the extremal length of a certain symmetric curve family. The existence of a critical point for the associated skinning map follows.


===Shinpei Baba (Caltech)===
''Grafting and complex projective structures''


A complex projective structure is a certain geometric structure on a (real) surface, and it corresponds a representation from the fundamental group of the base surface into PSL(2,C).  We discuss about a certain surgery operation, called a 2&pi;&ndash;grafting, which produces a different projective structure, preserving its holonomy representation.
This surgery is closely related to three-dimensional hyperbolic geometry.


===Kathryn Mann (Chicago)===
''The group structure of diffeomorphism groups''


Abstract:
What is the relationship between manifolds and the structure of their
diffeomorphism groups?
On the positive side, a remarkable theorem of Filipkiewicz says that the
group structure determines the manifold: if Diff(M) and Diff(N) are
isomorphic, then M and N are diffeomorphic.
On the negative side, we know little else.  Could the group Diff(M) act by
diffeomorphisms on M in nonstandard ways?  Does the "size" of Diff(M) say
anything about the complexity of M?  Ghys asked if M and N are manifolds,
and the group of compactly supported diffeomorphisms of N injects into the
group of compactly supported diffeomorphisms of M, can the dimension of M
be less than dim(N)?  We'll discuss these and other questions, and answer
these in the (already quite rich) case of dim(M)=1.




Revision as of 13:32, 14 August 2013

The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Richard Kent.

Hawk.jpg


Fall 2013

date speaker title host(s)
September 21
September 28
October 5
October 12
October 19
October 26
November 2
November 9
November 16
Thanksgiving Recess
November 30
December 7

Fall Abstracts

Spring 2014

date speaker title host(s)
January 25
February 1
February 8
February 15
February 22
March 1
March 8
March 15
Spring Break
April 5
April 19
April 26
May 3
May 10

Spring Abstracts

Archive of past Geometry seminars

2012-2013: Geometry_and_Topology_Seminar_2012-2013

2011-2012: Geometry_and_Topology_Seminar_2011-2012

2010: Fall-2010-Geometry-Topology

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