https://wiki.math.wisc.edu/api.php?action=feedcontributions&user=Gong&feedformat=atomUW-Math Wiki - User contributions [en]2022-05-25T19:36:41ZUser contributionsMediaWiki 1.30.1https://wiki.math.wisc.edu/index.php?title=Colloquia&diff=23062Colloquia2022-04-04T16:05:56Z<p>Gong: /* April 15, 2022, Bernhard Lamel, (Texas A&M University at Qatar) */</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, Friday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream], [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 />
'''Convergence and Divergence of Formal Power Series Maps'''<br />
<br />
Consider two real-analytic hypersurfaces (i.e. defined by convergent power series) in complex spaces. A formal holomorphic map is said to take one into the other if the composition of the power series defining the target with the map (which is just another formal power series) is a (formal) multiple of the defining power series of the source. In this talk, we are going to be interested in conditions for formal holomorphic maps to necessarily be convergent. Now, a formal holomorphic map taking the real line to itself is just a formal power series with real coefficients; this example also gives rise to real hypersurfaces in higher dimensional complex spaces having divergent formal self-maps. On the other hand, a formal map taking the unit sphere in higher dimensional complex space to itself is necessarily a rational map with poles outside of the sphere, in particular, the formal power series defining it converges. The convergence theory for formal self-maps of real hypersurfaces has been developed in the late 1990s and early 2000s. For formal embeddings, “ideal" conditions had been long conjectured. I’m going to give an introduction to this problem and talk about some joint work from 2018 with Nordine Mir giving a basically complete answer to the question when a formal map taking a real-analytic hypersurface in complex space into another one is necessarily convergent.<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>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=22972Analysis Seminar2022-03-17T15:08:16Z<p>Gong: </p>
<hr />
<div><br />
The 2021-2022 Analysis Seminar will be organized by David Beltran and Andreas Seeger.<br />
Some of the talks will be in person (room Van Vleck B139) and some will be online. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).<br />
<br />
Zoom links will be sent to those who have signed up for the Analysis Seminar List. 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. If you are from an institution different than UW-Madison, please send as well as an additional email to David and Andreas (dbeltran, seeger at math (dot) wisc (dot) edu) to notify the request.<br />
<br />
If you'd like to suggest speakers for the spring semester please contact David and Andreas.<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 21, VV B139<br />
| Dóminique Kemp<br />
| UW-Madison<br />
|[[#Dóminique Kemp | Decoupling by way of approximation ]]<br />
| <br />
|-<br />
|September 28, VV B139<br />
| Jack Burkart<br />
| UW-Madison<br />
|[[#Jack Burkart | Transcendental Julia Sets with Fractional Packing Dimension ]]<br />
| <br />
|-<br />
|October 5, Online<br />
| Giuseppe Negro<br />
| University of Birmingham<br />
|[[#Giuseppe Negro | Stability of sharp Fourier restriction to spheres ]]<br />
| <br />
|-<br />
|October 12, VV B139<br />
|Rajula Srivastava<br />
|UW Madison<br />
|[[#Rajula Srivastava | Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups ]]<br />
| <br />
|-<br />
|October 19, Online<br />
|Itamar Oliveira<br />
|Cornell University <br />
|[[#Itamar Oliveira | A new approach to the Fourier extension problem for the paraboloid ]]<br />
| <br />
|-<br />
|October 26, VV B139<br />
| Changkeun Oh<br />
| UW Madison<br />
|[[#Changkeun Oh | Decoupling inequalities for quadratic forms and beyond ]]<br />
| <br />
|-<br />
|October 29, Colloquium<br />
| Alexandru Ionescu <br />
| Princeton University<br />
|[[#Alexandru Ionescu | Polynomial averages and pointwise ergodic theorems on nilpotent groups]]<br />
|-<br />
|November 2, VV B139<br />
| Liding Yao<br />
| UW Madison<br />
|[[#Liding Yao | An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains ]]<br />
| <br />
|-<br />
|November 9, VV B139<br />
| Lingxiao Zhang<br />
| UW Madison<br />
|[[#Lingxiao Zhang | Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition ]]<br />
| <br />
|-<br />
|November 12, Colloquium<br />
| Kasso Okoudjou <br />
| Tufts University<br />
|[[#Kasso Okoudjou | An exploration in analysis on fractals ]]<br />
|-<br />
|November 16, VV B139<br />
| Rahul Parhi<br />
| UW Madison (EE)<br />
|[[#Rahul Parhi | On BV Spaces, Splines, and Neural Networks ]]<br />
| <br />
|-<br />
|November 30, VV B139<br />
| Alexei Poltoratski<br />
| UW Madison<br />
|[[#Alexei Poltoratski | Pointwise convergence for the scattering data and non-linear Fourier transform. ]]<br />
| <br />
|-<br />
|December 7, Online<br />
| John Green<br />
| The University of Edinburgh<br />
|[[#John Green | Estimates for oscillatory integrals via sublevel set estimates ]]<br />
| <br />
|-<br />
|December 14, VV B139<br />
| Tao Mei<br />
| Baylor University<br />
|[[#Tao Mei | Fourier Multipliers on free groups ]]<br />
| <br />
|-<br />
|Winter break<br />
|<br />
|<br />
|-<br />
|February 8, VV B139<br />
|Alexander Nagel <br />
| UW Madison<br />
|[[#Alex Nagel | Global estimates for a class of kernels and multipliers with multiple homogeneities]]<br />
| <br />
|-<br />
|February 15, Online<br />
| Sebastian Bechtel<br />
| Institut de Mathématiques de Bordeaux<br />
|[[#Sebastian Bechtel | Square roots of elliptic systems on open sets]]<br />
| <br />
|-<br />
| Friday, February 18, 4.pm, Colloquium<br />
| Andreas Seeger<br />
| UW Madison<br />
|[[#Andreas Seeger | Spherical maximal functions and fractal dimensions of dilation sets]]<br />
| <br />
|-<br />
|February 22, VV B139<br />
|Tongou Yang<br />
|University of British Comlumbia<br />
|[[#linktoabstract | Restricted projections along $C^2$ curves on the sphere ]]<br />
| <br />
|-<br />
|Monday, February 28, 4:30 p.m., Online<br />
| Po Lam Yung<br />
| Australian National University <br />
|[[#Po Lam Yung | Revisiting an old argument for Vinogradov's Mean Value Theorem ]]<br />
| <br />
|-<br />
|March 8, VV B139<br />
| Brian Street<br />
| UW Madison<br />
|[[#Brian Street | Maximal Subellipticity ]]<br />
| <br />
|-<br />
|March 15: No Seminar<br />
| <br />
| <br />
|<br />
| <br />
|-<br />
|March 22<br />
| Laurent Stolovitch<br />
| University of Cote d'Azur<br />
|[[#linktoabstract | Classification of reversible parabolic diffeomorphisms of<br />
$(\mathbb{C}^2,0)$ and of flat CR-singularities of exceptional<br />
hyperbolic type ]]<br />
| <br />
|-<br />
|March 29<br />
|Betsy Stovall <br />
|UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 5, Online<br />
|Malabika Pramanik<br />
|University of British Columbia<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 12<br />
| Hongki Jung<br />
| IU Bloomington<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 15, Colloquium<br />
| Bernhard Lamel<br />
| Texas A&M University at Qatar<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 19: No seminar<br />
| <br />
| <br />
|<br />
| <br />
|-<br />
|April 25, 4:00 p.m., Distinguished Lecture Series <br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 26, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 27, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|May 3<br />
| Jingjing Huang<br />
| University of Nevada, Reno <br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|Talks in the Fall semester 2022: <br />
|-<br />
|September 20, PDE and Analysis Seminar<br />
|Andrej Zlatoš<br />
|UCSD<br />
|[[#linktoabstract | Title ]]<br />
| Hung Tran<br />
|-<br />
|Friday, September 23, 4:00 p.m., Colloquium<br />
|Pablo Shmerkin <br />
|University of British Columbia<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
<br />
|}<br />
<br />
=Abstracts=<br />
===Dóminique Kemp===<br />
<br />
Decoupling by way of approximation<br />
<br />
Since Bourgain and Demeter's seminal 2017 decoupling result for nondegenerate hypersurfaces, several attempts have been made to extend the theory to degenerate hypersurfaces $M$. In this talk, we will discuss using surfaces derived from the local Taylor expansions of $M$ in order to obtain "approximate" decoupling results. By themselves, these approximate decouplings do not avail much. However, upon considerate iteration, for a specifically chosen $M$, they culminate in a decoupling partition of $M$ into caps small enough either as originally desired or otherwise genuinely nondegenerate at the local scale. A key feature that will be discussed is the notion of approximating a non-convex hypersurface $M$ by convex hypersurfaces at various scales. In this manner, contrary to initial intuition, non-trivial $\ell^2$ decoupling results will be obtained for $M$.<br />
<br />
===Jack Burkart===<br />
<br />
Transcendental Julia Sets with Fractional Packing Dimension<br />
<br />
If f is an entire function, the Julia set of f is the set of all points such that f and its iterates locally do not form a normal family; nearby points have very different orbits under iteration by f. A topic of interest in complex dynamics is studying the fractal geometry of the Julia set.<br />
<br />
In this talk, we will discuss my thesis result where I construct non-polynomial (transcendental) entire functions whose Julia set has packing dimension strictly between (1,2). We will introduce various notions of dimension and basic objects in complex dynamics, and discuss a history of dimension results in complex dynamics. We will discuss some key aspects of the proof, which include a use of Whitney decompositions of domains as a tool to calculate the packing dimension, and some open questions I am thinking about.<br />
<br />
===Giuseppe Negro===<br />
<br />
Stability of sharp Fourier restriction to spheres<br />
<br />
In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate. <br />
<br />
Joint work with E.Carneiro and D.Oliveira e Silva.<br />
<br />
===Rajula Srivastava===<br />
<br />
Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups<br />
<br />
We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.<br />
<br />
===Itamar Oliveira===<br />
<br />
A new approach to the Fourier extension problem for the paraboloid<br />
<br />
An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $ of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.<br />
<br />
===Changkeun Oh===<br />
<br />
Decoupling inequalities for quadratic forms and beyond<br />
<br />
In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.<br />
<br />
===Alexandru Ionescu===<br />
<br />
Polynomial averages and pointwise ergodic theorems on nilpotent groups<br />
<br />
I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.<br />
<br />
===Liding Yao===<br />
<br />
An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains<br />
<br />
Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.<br />
<br />
===Lingxiao Zhang===<br />
<br />
Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition<br />
<br />
We study operators of the form<br />
$Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$ <br />
where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.<br />
<br />
===Kasso Okoudjou===<br />
<br />
An exploration in analysis on fractals<br />
<br />
Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.<br />
<br />
===Rahul Parhi===<br />
<br />
On BV Spaces, Splines, and Neural Networks<br />
<br />
Many problems in science and engineering can be phrased as the problem<br />
of reconstructing a function from a finite number of possibly noisy<br />
measurements. The reconstruction problem is inherently ill-posed when<br />
the allowable functions belong to an infinite set. Classical techniques<br />
to solve this problem assume, a priori, that the underlying function has<br />
some kind of regularity, typically Sobolev, Besov, or BV regularity. The<br />
field of applied harmonic analysis is interested in studying efficient<br />
decompositions and representations for functions with certain<br />
regularity. Common representation systems are based on splines and<br />
wavelets. These are well understood mathematically and have been<br />
successfully applied in a variety of signal processing and statistical<br />
tasks. Neural networks are another type of representation system that is<br />
useful in practice, but poorly understood mathematically.<br />
<br />
In this talk, I will discuss my research which aims to rectify this<br />
issue by understanding the regularity properties of neural networks in a<br />
similar vein to classical methods based on splines and wavelets. In<br />
particular, we will show that neural networks are optimal solutions to<br />
variational problems over BV-type function spaces defined via the Radon<br />
transform. These spaces are non-reflexive Banach spaces, generally<br />
distinct from classical spaces studied in analysis. However, in the<br />
univariate setting, neural networks reduce to splines and these function<br />
spaces reduce to classical univariate BV spaces. If time permits, I will<br />
also discuss approximation properties of these spaces, showing that they<br />
are, in some sense, "small" compared to classical multivariate spaces<br />
such as Sobolev or Besov spaces.<br />
<br />
This is joint work with Robert Nowak.<br />
<br />
===Alexei Poltoratski===<br />
<br />
Title: Pointwise convergence for the scattering data and non-linear Fourier transform.<br />
<br />
Abstract: This talk is about applications of complex and harmonic analysis in spectral and scattering theory<br />
for differential operators. The scattering transform for the Dirac system of differential equations<br />
can be viewed as the non-linear version of the classical Fourier transform. This connection raises many natural<br />
problems on extensions of classical results of Fourier analysis to non-linear settings. In this talk<br />
I will discuss one of such problems, an extension of Carleson's theorem on pointwise convergence of Fourier series to the non-linear case.<br />
<br />
===John Green===<br />
<br />
Estimates for oscillatory integrals via sublevel set estimates.<br />
<br />
In many situations, oscillatory integral estimates are known to imply sublevel set estimates in a stable manner. Reversing this implication is much more difficult, but understanding when this is true is helpful for understanding scalar oscillatory integral estimates. We shall motivate a line of investigation in which we seek to reverse the implication in the presence of a qualitative structural assumption. After considering some one-dimensional results, we turn to the setting of convex functions in higher dimensions.<br />
<br />
===Tao Mei===<br />
<br />
Fourier Multipliers on free groups.<br />
<br />
In this introductory talk, I will try to explain what is the noncommutative Lp spaces associated with the free groups, and what are the to be answered questions on the corresponding Fourier multiplier operators. At the end, I will explain a recent work on an analogue of Mikhlin’s Lp Fourier multiplier theory on free groups (joint with Eric Ricard and Quanhua Xu).<br />
<br />
===Alex Nagel===<br />
<br />
Global estimates for a class of kernels and multipliers with multiple homogeneities<br />
<br />
In joint work with Fulvio Ricci we obtain global estimates for a class of kernels and multipliers which contain homogeneous Calderon-Zygmund operators for several different homogeneities. This is an extension of earlier work with Ricci, Stein, and Wainger on the local theory.<br />
<br />
===Sebastian Bechtel===<br />
<br />
Square roots of elliptic systems on open sets<br />
<br />
In my talk, we will consider elliptic systems in divergence form with measurable and elliptic complex coefficients on possibly unbounded open sets which are subject to mixed boundary conditions. First, I will present and discuss minimal geometric conditions under which Kato’s square root problem can be solved. In particular, I will present an argument that allows to work on a set that is not supposed to satisfy the interior thickness condition.<br />
Afterwards, we will investigate the question for which integrability parameters p the square root isomorphism $W^{1,2} \to L^2$ extrapolates to an isomorphism $W^{1,p} \to L^p$. We focus on the case $p>2$. I will introduce a critical number that describes the range in which $L$ (compatibly) acts as an isomorphism $W^{1,p} \to W^{-1,p}$. We will then see that this critical number also yields an optimal range in which the square root extrapolates to a $p$-isomorphism, even in the case of mixed boundary conditions.<br />
<br />
===Tongou Yang===<br />
<br />
Restricted projections along $C^2$ curves on the sphere<br />
<br />
Given a $C^2$ closed curve $\gamma(\theta)$ lying on the sphere<br />
$\mathbb S^2$ and a Borel set $A\subseteq \mathbb R^3$. Consider the<br />
projections $P_\theta(A)$ of $A$ into straight lines in the directions<br />
$\gamma(\theta)$. We prove that if $\gamma$ satisfies the torsion<br />
condition: $\det(\gamma,\gamma',\gamma")(\theta)\neq 0$ for any $\theta$,<br />
then for almost every $\theta$, the Hausdorff dimension of $P_\theta(A)$ is<br />
equal to $\min\{1,\dim_H(A)\}$. This solves a conjecture of Fässler and<br />
Orponen. One key feature of our argument is a result of Marcus-Tardos in<br />
topological graph theory. This is a joint work with Malabika Pramanik, Orit Raz and Josh Zahl.<br />
<br />
===Po Lam Yung===<br />
<br />
Revisiting an old argument for Vinogradov's Mean Value Theorem<br />
<br />
We will examine an old argument for the Vinogradov's Mean Value Theorem due to Karatsuba, and interpret it in the language of Fourier decoupling. This is ongoing work in progress with Brian Cook, Kevin Hughes, Zane Kun Li, Akshat Mudgal and Olivier Robert.<br />
<br />
===Brian Street===<br />
<br />
Maximal Subellipticity<br />
<br />
The theory of elliptic PDEs stands apart from many other areas of PDEs because sharp results are known for very general linear and fully nonlinear elliptic PDEs. Many of the classical techniques from harmonic analysis were first developed to prove these sharp results; and the study of elliptic PDEs leans heavily on the Fourier transform and Riemannian geometry. Starting with work of Hörmander, Kohn, Folland, Stein, and Rothschild in the 60s and 70s, a far-reaching generalization of ellipticity was introduced: now known as maximal subellipticity or maximal hypoellipticity. In the intervening years, many authors have adapted results from elliptic PDEs to various special cases of maximally subelliptic PDEs. Where elliptic operators are connected to Riemannian geometry, maximally subelliptic operators are connected to sub-Riemannian geometry. The Fourier transform is no longer a central tool but can be replaced with more modern tools from harmonic analysis.<br />
<br />
===Laurent Stolovitch===<br />
<br />
Classification of reversible parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ and of flat CR-singularities of exceptional hyperbolic type<br />
<br />
The aim of this joint work with Martin Klimes is twofold:<br />
<br />
First we study holomorphic germs of parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ that are reversed by a holomorphic reflection and posses an analytic first integral with non-degenerate critical point at the origin. We find a canonical formal normal form and provide a complete analytic classification (in formal generic cases) in terms of a collection of functional invariants.<br />
<br />
Related to it, we solve the problem of both formal and analytic classification of germs of real analytic surfaces in $\mathbb{C}^2$ with non-degenerate CR singularities of exceptional hyperbolic type, under the assumption that the surface is holomorphically flat, i.e. that it can be locally holomorphically embedded in a real hypersurface of $\mathbb{C}^2$.<br />
<br />
=[[Previous_Analysis_seminars]]=<br />
<br />
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars<br />
<br />
=Extras=<br />
<br />
[[Blank Analysis Seminar Template]]<br />
<br />
<br />
Graduate Student Seminar:<br />
<br />
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=22971Analysis Seminar2022-03-17T15:06:46Z<p>Gong: </p>
<hr />
<div><br />
The 2021-2022 Analysis Seminar will be organized by David Beltran and Andreas Seeger.<br />
Some of the talks will be in person (room Van Vleck B139) and some will be online. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).<br />
<br />
Zoom links will be sent to those who have signed up for the Analysis Seminar List. 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. If you are from an institution different than UW-Madison, please send as well as an additional email to David and Andreas (dbeltran, seeger at math (dot) wisc (dot) edu) to notify the request.<br />
<br />
If you'd like to suggest speakers for the spring semester please contact David and Andreas.<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 21, VV B139<br />
| Dóminique Kemp<br />
| UW-Madison<br />
|[[#Dóminique Kemp | Decoupling by way of approximation ]]<br />
| <br />
|-<br />
|September 28, VV B139<br />
| Jack Burkart<br />
| UW-Madison<br />
|[[#Jack Burkart | Transcendental Julia Sets with Fractional Packing Dimension ]]<br />
| <br />
|-<br />
|October 5, Online<br />
| Giuseppe Negro<br />
| University of Birmingham<br />
|[[#Giuseppe Negro | Stability of sharp Fourier restriction to spheres ]]<br />
| <br />
|-<br />
|October 12, VV B139<br />
|Rajula Srivastava<br />
|UW Madison<br />
|[[#Rajula Srivastava | Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups ]]<br />
| <br />
|-<br />
|October 19, Online<br />
|Itamar Oliveira<br />
|Cornell University <br />
|[[#Itamar Oliveira | A new approach to the Fourier extension problem for the paraboloid ]]<br />
| <br />
|-<br />
|October 26, VV B139<br />
| Changkeun Oh<br />
| UW Madison<br />
|[[#Changkeun Oh | Decoupling inequalities for quadratic forms and beyond ]]<br />
| <br />
|-<br />
|October 29, Colloquium<br />
| Alexandru Ionescu <br />
| Princeton University<br />
|[[#Alexandru Ionescu | Polynomial averages and pointwise ergodic theorems on nilpotent groups]]<br />
|-<br />
|November 2, VV B139<br />
| Liding Yao<br />
| UW Madison<br />
|[[#Liding Yao | An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains ]]<br />
| <br />
|-<br />
|November 9, VV B139<br />
| Lingxiao Zhang<br />
| UW Madison<br />
|[[#Lingxiao Zhang | Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition ]]<br />
| <br />
|-<br />
|November 12, Colloquium<br />
| Kasso Okoudjou <br />
| Tufts University<br />
|[[#Kasso Okoudjou | An exploration in analysis on fractals ]]<br />
|-<br />
|November 16, VV B139<br />
| Rahul Parhi<br />
| UW Madison (EE)<br />
|[[#Rahul Parhi | On BV Spaces, Splines, and Neural Networks ]]<br />
| <br />
|-<br />
|November 30, VV B139<br />
| Alexei Poltoratski<br />
| UW Madison<br />
|[[#Alexei Poltoratski | Pointwise convergence for the scattering data and non-linear Fourier transform. ]]<br />
| <br />
|-<br />
|December 7, Online<br />
| John Green<br />
| The University of Edinburgh<br />
|[[#John Green | Estimates for oscillatory integrals via sublevel set estimates ]]<br />
| <br />
|-<br />
|December 14, VV B139<br />
| Tao Mei<br />
| Baylor University<br />
|[[#Tao Mei | Fourier Multipliers on free groups ]]<br />
| <br />
|-<br />
|Winter break<br />
|<br />
|<br />
|-<br />
|February 8, VV B139<br />
|Alexander Nagel <br />
| UW Madison<br />
|[[#Alex Nagel | Global estimates for a class of kernels and multipliers with multiple homogeneities]]<br />
| <br />
|-<br />
|February 15, Online<br />
| Sebastian Bechtel<br />
| Institut de Mathématiques de Bordeaux<br />
|[[#Sebastian Bechtel | Square roots of elliptic systems on open sets]]<br />
| <br />
|-<br />
| Friday, February 18, 4.pm, Colloquium<br />
| Andreas Seeger<br />
| UW Madison<br />
|[[#Andreas Seeger | Spherical maximal functions and fractal dimensions of dilation sets]]<br />
| <br />
|-<br />
|February 22, VV B139<br />
|Tongou Yang<br />
|University of British Comlumbia<br />
|[[#linktoabstract | Restricted projections along $C^2$ curves on the sphere ]]<br />
| <br />
|-<br />
|Monday, February 28, 4:30 p.m., Online<br />
| Po Lam Yung<br />
| Australian National University <br />
|[[#Po Lam Yung | Revisiting an old argument for Vinogradov's Mean Value Theorem ]]<br />
| <br />
|-<br />
|March 8, VV B139<br />
| Brian Street<br />
| UW Madison<br />
|[[#Brian Street | Maximal Subellipticity ]]<br />
| <br />
|-<br />
|March 15: No Seminar<br />
| <br />
| <br />
|<br />
| <br />
|-<br />
|March 22<br />
| Laurent Stolovitch<br />
| University of Cote d'Azur<br />
|[[#linktoabstract | Classification of reversible parabolic diffeomorphisms of<br />
$(\mathbb{C}^2,0)$ and of flat CR-singularities of exceptional<br />
hyperbolic type ]]<br />
| <br />
|-<br />
|March 29<br />
|Betsy Stovall <br />
|UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 5, Online<br />
|Malabika Pramanik<br />
|University of British Columbia<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 12<br />
| Hongki Jung<br />
| IU Bloomington<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 15, Colloquium<br />
| Bernhard Lamel<br />
| Texas A&M University at Qatar<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 19: No seminar<br />
| <br />
| <br />
|<br />
| <br />
|-<br />
|April 25, 4:00 p.m., Distinguished Lecture Series <br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 26, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 27, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|May 3<br />
| Jingjing Huang<br />
| University of Nevada, Reno <br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|Talks in the Fall semester 2022: <br />
|-<br />
|September 20, PDE and Analysis Seminar<br />
|Andrej Zlatoš<br />
|UCSD<br />
|[[#linktoabstract | Title ]]<br />
| Hung Tran<br />
|-<br />
|Friday, September 23, 4:00 p.m., Colloquium<br />
|Pablo Shmerkin <br />
|University of British Columbia<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
<br />
|}<br />
<br />
=Abstracts=<br />
===Dóminique Kemp===<br />
<br />
Decoupling by way of approximation<br />
<br />
Since Bourgain and Demeter's seminal 2017 decoupling result for nondegenerate hypersurfaces, several attempts have been made to extend the theory to degenerate hypersurfaces $M$. In this talk, we will discuss using surfaces derived from the local Taylor expansions of $M$ in order to obtain "approximate" decoupling results. By themselves, these approximate decouplings do not avail much. However, upon considerate iteration, for a specifically chosen $M$, they culminate in a decoupling partition of $M$ into caps small enough either as originally desired or otherwise genuinely nondegenerate at the local scale. A key feature that will be discussed is the notion of approximating a non-convex hypersurface $M$ by convex hypersurfaces at various scales. In this manner, contrary to initial intuition, non-trivial $\ell^2$ decoupling results will be obtained for $M$.<br />
<br />
===Jack Burkart===<br />
<br />
Transcendental Julia Sets with Fractional Packing Dimension<br />
<br />
If f is an entire function, the Julia set of f is the set of all points such that f and its iterates locally do not form a normal family; nearby points have very different orbits under iteration by f. A topic of interest in complex dynamics is studying the fractal geometry of the Julia set.<br />
<br />
In this talk, we will discuss my thesis result where I construct non-polynomial (transcendental) entire functions whose Julia set has packing dimension strictly between (1,2). We will introduce various notions of dimension and basic objects in complex dynamics, and discuss a history of dimension results in complex dynamics. We will discuss some key aspects of the proof, which include a use of Whitney decompositions of domains as a tool to calculate the packing dimension, and some open questions I am thinking about.<br />
<br />
===Giuseppe Negro===<br />
<br />
Stability of sharp Fourier restriction to spheres<br />
<br />
In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate. <br />
<br />
Joint work with E.Carneiro and D.Oliveira e Silva.<br />
<br />
===Rajula Srivastava===<br />
<br />
Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups<br />
<br />
We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.<br />
<br />
===Itamar Oliveira===<br />
<br />
A new approach to the Fourier extension problem for the paraboloid<br />
<br />
An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $ of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.<br />
<br />
===Changkeun Oh===<br />
<br />
Decoupling inequalities for quadratic forms and beyond<br />
<br />
In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.<br />
<br />
===Alexandru Ionescu===<br />
<br />
Polynomial averages and pointwise ergodic theorems on nilpotent groups<br />
<br />
I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.<br />
<br />
===Liding Yao===<br />
<br />
An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains<br />
<br />
Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.<br />
<br />
===Lingxiao Zhang===<br />
<br />
Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition<br />
<br />
We study operators of the form<br />
$Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$ <br />
where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.<br />
<br />
===Kasso Okoudjou===<br />
<br />
An exploration in analysis on fractals<br />
<br />
Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.<br />
<br />
===Rahul Parhi===<br />
<br />
On BV Spaces, Splines, and Neural Networks<br />
<br />
Many problems in science and engineering can be phrased as the problem<br />
of reconstructing a function from a finite number of possibly noisy<br />
measurements. The reconstruction problem is inherently ill-posed when<br />
the allowable functions belong to an infinite set. Classical techniques<br />
to solve this problem assume, a priori, that the underlying function has<br />
some kind of regularity, typically Sobolev, Besov, or BV regularity. The<br />
field of applied harmonic analysis is interested in studying efficient<br />
decompositions and representations for functions with certain<br />
regularity. Common representation systems are based on splines and<br />
wavelets. These are well understood mathematically and have been<br />
successfully applied in a variety of signal processing and statistical<br />
tasks. Neural networks are another type of representation system that is<br />
useful in practice, but poorly understood mathematically.<br />
<br />
In this talk, I will discuss my research which aims to rectify this<br />
issue by understanding the regularity properties of neural networks in a<br />
similar vein to classical methods based on splines and wavelets. In<br />
particular, we will show that neural networks are optimal solutions to<br />
variational problems over BV-type function spaces defined via the Radon<br />
transform. These spaces are non-reflexive Banach spaces, generally<br />
distinct from classical spaces studied in analysis. However, in the<br />
univariate setting, neural networks reduce to splines and these function<br />
spaces reduce to classical univariate BV spaces. If time permits, I will<br />
also discuss approximation properties of these spaces, showing that they<br />
are, in some sense, "small" compared to classical multivariate spaces<br />
such as Sobolev or Besov spaces.<br />
<br />
This is joint work with Robert Nowak.<br />
<br />
===Alexei Poltoratski===<br />
<br />
Title: Pointwise convergence for the scattering data and non-linear Fourier transform.<br />
<br />
Abstract: This talk is about applications of complex and harmonic analysis in spectral and scattering theory<br />
for differential operators. The scattering transform for the Dirac system of differential equations<br />
can be viewed as the non-linear version of the classical Fourier transform. This connection raises many natural<br />
problems on extensions of classical results of Fourier analysis to non-linear settings. In this talk<br />
I will discuss one of such problems, an extension of Carleson's theorem on pointwise convergence of Fourier series to the non-linear case.<br />
<br />
===John Green===<br />
<br />
Estimates for oscillatory integrals via sublevel set estimates.<br />
<br />
In many situations, oscillatory integral estimates are known to imply sublevel set estimates in a stable manner. Reversing this implication is much more difficult, but understanding when this is true is helpful for understanding scalar oscillatory integral estimates. We shall motivate a line of investigation in which we seek to reverse the implication in the presence of a qualitative structural assumption. After considering some one-dimensional results, we turn to the setting of convex functions in higher dimensions.<br />
<br />
===Tao Mei===<br />
<br />
Fourier Multipliers on free groups.<br />
<br />
In this introductory talk, I will try to explain what is the noncommutative Lp spaces associated with the free groups, and what are the to be answered questions on the corresponding Fourier multiplier operators. At the end, I will explain a recent work on an analogue of Mikhlin’s Lp Fourier multiplier theory on free groups (joint with Eric Ricard and Quanhua Xu).<br />
<br />
===Alex Nagel===<br />
<br />
Global estimates for a class of kernels and multipliers with multiple homogeneities<br />
<br />
In joint work with Fulvio Ricci we obtain global estimates for a class of kernels and multipliers which contain homogeneous Calderon-Zygmund operators for several different homogeneities. This is an extension of earlier work with Ricci, Stein, and Wainger on the local theory.<br />
<br />
===Sebastian Bechtel===<br />
<br />
Square roots of elliptic systems on open sets<br />
<br />
In my talk, we will consider elliptic systems in divergence form with measurable and elliptic complex coefficients on possibly unbounded open sets which are subject to mixed boundary conditions. First, I will present and discuss minimal geometric conditions under which Kato’s square root problem can be solved. In particular, I will present an argument that allows to work on a set that is not supposed to satisfy the interior thickness condition.<br />
Afterwards, we will investigate the question for which integrability parameters p the square root isomorphism $W^{1,2} \to L^2$ extrapolates to an isomorphism $W^{1,p} \to L^p$. We focus on the case $p>2$. I will introduce a critical number that describes the range in which $L$ (compatibly) acts as an isomorphism $W^{1,p} \to W^{-1,p}$. We will then see that this critical number also yields an optimal range in which the square root extrapolates to a $p$-isomorphism, even in the case of mixed boundary conditions.<br />
<br />
===Tongou Yang===<br />
<br />
Restricted projections along $C^2$ curves on the sphere<br />
<br />
Given a $C^2$ closed curve $\gamma(\theta)$ lying on the sphere<br />
$\mathbb S^2$ and a Borel set $A\subseteq \mathbb R^3$. Consider the<br />
projections $P_\theta(A)$ of $A$ into straight lines in the directions<br />
$\gamma(\theta)$. We prove that if $\gamma$ satisfies the torsion<br />
condition: $\det(\gamma,\gamma',\gamma")(\theta)\neq 0$ for any $\theta$,<br />
then for almost every $\theta$, the Hausdorff dimension of $P_\theta(A)$ is<br />
equal to $\min\{1,\dim_H(A)\}$. This solves a conjecture of Fässler and<br />
Orponen. One key feature of our argument is a result of Marcus-Tardos in<br />
topological graph theory. This is a joint work with Malabika Pramanik, Orit Raz and Josh Zahl.<br />
<br />
===Po Lam Yung===<br />
<br />
Revisiting an old argument for Vinogradov's Mean Value Theorem<br />
<br />
We will examine an old argument for the Vinogradov's Mean Value Theorem due to Karatsuba, and interpret it in the language of Fourier decoupling. This is ongoing work in progress with Brian Cook, Kevin Hughes, Zane Kun Li, Akshat Mudgal and Olivier Robert.<br />
<br />
===Brian Street===<br />
<br />
Maximal Subellipticity<br />
<br />
The theory of elliptic PDEs stands apart from many other areas of PDEs because sharp results are known for very general linear and fully nonlinear elliptic PDEs. Many of the classical techniques from harmonic analysis were first developed to prove these sharp results; and the study of elliptic PDEs leans heavily on the Fourier transform and Riemannian geometry. Starting with work of Hörmander, Kohn, Folland, Stein, and Rothschild in the 60s and 70s, a far-reaching generalization of ellipticity was introduced: now known as maximal subellipticity or maximal hypoellipticity. In the intervening years, many authors have adapted results from elliptic PDEs to various special cases of maximally subelliptic PDEs. Where elliptic operators are connected to Riemannian geometry, maximally subelliptic operators are connected to sub-Riemannian geometry. The Fourier transform is no longer a central tool but can be replaced with more modern tools from harmonic analysis.<br />
<br />
===Laurent Stolovitch===<br />
<br />
Classification of reversible parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ and of flat CR-singularities of exceptional hyperbolic type<br />
<br />
The aim of this joint work with Martin Klimes is twofold:<br />
<br />
First we study holomorphic germs of parabolic diffeomorphisms of $(\mathbb{C}^2,0)$ that are reversed by a holomorphic reflection and posses an analytic first integral with non-degenerate critical point at the origin. We find a canonical formal normal form and provide a complete analytic classification (in formal generic cases) in terms of a collection of functional invariants.<br />
<br />
Related to it, we solve the problem of both formal and analytic classification of germs of real analytic surfaces in $\C^2$ with non-degenerate CR singularities of exceptional hyperbolic type, under the assumption that the surface is holomorphically flat, i.e. that it can be locally holomorphically embedded in a real hypersurface of $\C^2$.<br />
<br />
=[[Previous_Analysis_seminars]]=<br />
<br />
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars<br />
<br />
=Extras=<br />
<br />
[[Blank Analysis Seminar Template]]<br />
<br />
<br />
Graduate Student Seminar:<br />
<br />
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=22567Analysis Seminar2022-01-25T23:39:08Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div><br />
The 2021-2022 Analysis Seminar will be organized by David Beltran and Andreas Seeger.<br />
Some of the talks will be in person (room Van Vleck B139) and some will be online. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).<br />
<br />
Zoom links will be sent to those who have signed up for the Analysis Seminar List. 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. If you are from an institution different than UW-Madison, please send as well as an additional email to David and Andreas (dbeltran, seeger at math (dot) wisc (dot) edu) to notify the request.<br />
<br />
If you'd like to suggest speakers for the spring semester please contact David and Andreas.<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 21, VV B139<br />
| Dóminique Kemp<br />
| UW-Madison<br />
|[[#Dóminique Kemp | Decoupling by way of approximation ]]<br />
| <br />
|-<br />
|September 28, VV B139<br />
| Jack Burkart<br />
| UW-Madison<br />
|[[#Jack Burkart | Transcendental Julia Sets with Fractional Packing Dimension ]]<br />
| <br />
|-<br />
|October 5, Online<br />
| Giuseppe Negro<br />
| University of Birmingham<br />
|[[#Giuseppe Negro | Stability of sharp Fourier restriction to spheres ]]<br />
| <br />
|-<br />
|October 12, VV B139<br />
|Rajula Srivastava<br />
|UW Madison<br />
|[[#Rajula Srivastava | Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups ]]<br />
| <br />
|-<br />
|October 19, Online<br />
|Itamar Oliveira<br />
|Cornell University <br />
|[[#Itamar Oliveira | A new approach to the Fourier extension problem for the paraboloid ]]<br />
| <br />
|-<br />
|October 26, VV B139<br />
| Changkeun Oh<br />
| UW Madison<br />
|[[#Changkeun Oh | Decoupling inequalities for quadratic forms and beyond ]]<br />
| <br />
|-<br />
|October 29, Colloquium<br />
| Alexandru Ionescu <br />
| Princeton University<br />
|[[#Alexandru Ionescu | Polynomial averages and pointwise ergodic theorems on nilpotent groups]]<br />
|-<br />
|November 2, VV B139<br />
| Liding Yao<br />
| UW Madison<br />
|[[#Liding Yao | An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains ]]<br />
| <br />
|-<br />
|November 9, VV B139<br />
| Lingxiao Zhang<br />
| UW Madison<br />
|[[#Lingxiao Zhang | Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition ]]<br />
| <br />
|-<br />
|November 12, Colloquium<br />
| Kasso Okoudjou <br />
| Tufts University<br />
|[[#Kasso Okoudjou | An exploration in analysis on fractals ]]<br />
|-<br />
|November 16, VV B139<br />
| Rahul Parhi<br />
| UW Madison (EE)<br />
|[[#Rahul Parhi | On BV Spaces, Splines, and Neural Networks ]]<br />
| <br />
|-<br />
|November 30, VV B139<br />
| Alexei Poltoratski<br />
| UW Madison<br />
|[[#Alexei Poltoratski | Pointwise convergence for the scattering data and non-linear Fourier transform. ]]<br />
| <br />
|-<br />
|December 7, Online<br />
| John Green<br />
| The University of Edinburgh<br />
|[[#John Green | Estimates for oscillatory integrals via sublevel set estimates ]]<br />
| <br />
|-<br />
|December 14, VV B139<br />
| Tao Mei<br />
| Baylor University<br />
|[[#Tao Mei | Fourier Multipliers on free groups ]]<br />
| <br />
|-<br />
|Winter break<br />
|<br />
|<br />
|-<br />
|February 8, VV B139<br />
|Alex Nagel <br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|February 15, Online<br />
| Sebastian Bechtel<br />
| Institut de Mathématiques de Bordeaux<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|February 22, VV B139<br />
|Betsy Stovall <br />
|UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 1, Online<br />
| Po Lam Yung<br />
| Australian National University <br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 8, VV B139<br />
| Brian Street<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 15: No Seminar<br />
| <br />
| <br />
|<br />
| <br />
|-<br />
|March 22<br />
| Laurent Stolovitch<br />
| University of Cote d'Azur<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 29<br />
| TBA<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 5, Online<br />
|Malabika Pramanik<br />
|University of British Columbia<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 12<br />
| Hongki Jung<br />
| IU Bloomington<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 15, Colloquium<br />
| Bernhard Lamel<br />
| Texas A&M University at Qatar<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 19: No seminar<br />
| <br />
| <br />
|<br />
| <br />
|-<br />
|April 22, Colloquium<br />
|Detlef Müller<br />
|University of Kiel<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 25, 4:00 p.m., Distinguished Lecture Series <br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 26, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 27, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|May 3<br />
| Jingjing Huang<br />
| University of Nevada, Reno <br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|Talks in the Fall semester 2022: <br />
|-<br />
|September 20, PDE and Analysis Seminar<br />
|Andrej Zlatoš<br />
|UCSD<br />
|[[#linktoabstract | Title ]]<br />
| Hung Tran<br />
|-<br />
<br />
<br />
|}<br />
<br />
=Abstracts=<br />
===Dóminique Kemp===<br />
<br />
Decoupling by way of approximation<br />
<br />
Since Bourgain and Demeter's seminal 2017 decoupling result for nondegenerate hypersurfaces, several attempts have been made to extend the theory to degenerate hypersurfaces $M$. In this talk, we will discuss using surfaces derived from the local Taylor expansions of $M$ in order to obtain "approximate" decoupling results. By themselves, these approximate decouplings do not avail much. However, upon considerate iteration, for a specifically chosen $M$, they culminate in a decoupling partition of $M$ into caps small enough either as originally desired or otherwise genuinely nondegenerate at the local scale. A key feature that will be discussed is the notion of approximating a non-convex hypersurface $M$ by convex hypersurfaces at various scales. In this manner, contrary to initial intuition, non-trivial $\ell^2$ decoupling results will be obtained for $M$.<br />
<br />
===Jack Burkart===<br />
<br />
Transcendental Julia Sets with Fractional Packing Dimension<br />
<br />
If f is an entire function, the Julia set of f is the set of all points such that f and its iterates locally do not form a normal family; nearby points have very different orbits under iteration by f. A topic of interest in complex dynamics is studying the fractal geometry of the Julia set.<br />
<br />
In this talk, we will discuss my thesis result where I construct non-polynomial (transcendental) entire functions whose Julia set has packing dimension strictly between (1,2). We will introduce various notions of dimension and basic objects in complex dynamics, and discuss a history of dimension results in complex dynamics. We will discuss some key aspects of the proof, which include a use of Whitney decompositions of domains as a tool to calculate the packing dimension, and some open questions I am thinking about.<br />
<br />
===Giuseppe Negro===<br />
<br />
Stability of sharp Fourier restriction to spheres<br />
<br />
In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate. <br />
<br />
Joint work with E.Carneiro and D.Oliveira e Silva.<br />
<br />
===Rajula Srivastava===<br />
<br />
Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups<br />
<br />
We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.<br />
<br />
===Itamar Oliveira===<br />
<br />
A new approach to the Fourier extension problem for the paraboloid<br />
<br />
An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $ of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.<br />
<br />
===Changkeun Oh===<br />
<br />
Decoupling inequalities for quadratic forms and beyond<br />
<br />
In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.<br />
<br />
===Alexandru Ionescu===<br />
<br />
Polynomial averages and pointwise ergodic theorems on nilpotent groups<br />
<br />
I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.<br />
<br />
===Liding Yao===<br />
<br />
An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains<br />
<br />
Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.<br />
<br />
===Lingxiao Zhang===<br />
<br />
Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition<br />
<br />
We study operators of the form<br />
$Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$ <br />
where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.<br />
<br />
===Kasso Okoudjou===<br />
<br />
An exploration in analysis on fractals<br />
<br />
Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.<br />
<br />
===Rahul Parhi===<br />
<br />
On BV Spaces, Splines, and Neural Networks<br />
<br />
Many problems in science and engineering can be phrased as the problem<br />
of reconstructing a function from a finite number of possibly noisy<br />
measurements. The reconstruction problem is inherently ill-posed when<br />
the allowable functions belong to an infinite set. Classical techniques<br />
to solve this problem assume, a priori, that the underlying function has<br />
some kind of regularity, typically Sobolev, Besov, or BV regularity. The<br />
field of applied harmonic analysis is interested in studying efficient<br />
decompositions and representations for functions with certain<br />
regularity. Common representation systems are based on splines and<br />
wavelets. These are well understood mathematically and have been<br />
successfully applied in a variety of signal processing and statistical<br />
tasks. Neural networks are another type of representation system that is<br />
useful in practice, but poorly understood mathematically.<br />
<br />
In this talk, I will discuss my research which aims to rectify this<br />
issue by understanding the regularity properties of neural networks in a<br />
similar vein to classical methods based on splines and wavelets. In<br />
particular, we will show that neural networks are optimal solutions to<br />
variational problems over BV-type function spaces defined via the Radon<br />
transform. These spaces are non-reflexive Banach spaces, generally<br />
distinct from classical spaces studied in analysis. However, in the<br />
univariate setting, neural networks reduce to splines and these function<br />
spaces reduce to classical univariate BV spaces. If time permits, I will<br />
also discuss approximation properties of these spaces, showing that they<br />
are, in some sense, "small" compared to classical multivariate spaces<br />
such as Sobolev or Besov spaces.<br />
<br />
This is joint work with Robert Nowak.<br />
<br />
===Alexei Poltoratski===<br />
<br />
Title: Pointwise convergence for the scattering data and non-linear Fourier transform.<br />
<br />
Abstract: This talk is about applications of complex and harmonic analysis in spectral and scattering theory<br />
for differential operators. The scattering transform for the Dirac system of differential equations<br />
can be viewed as the non-linear version of the classical Fourier transform. This connection raises many natural<br />
problems on extensions of classical results of Fourier analysis to non-linear settings. In this talk<br />
I will discuss one of such problems, an extension of Carleson's theorem on pointwise convergence of Fourier series to the non-linear case.<br />
<br />
<br />
<br />
===John Green===<br />
<br />
Estimates for oscillatory integrals via sublevel set estimates.<br />
<br />
In many situations, oscillatory integral estimates are known to imply sublevel set estimates in a stable manner. Reversing this implication is much more difficult, but understanding when this is true is helpful for understanding scalar oscillatory integral estimates. We shall motivate a line of investigation in which we seek to reverse the implication in the presence of a qualitative structural assumption. After considering some one-dimensional results, we turn to the setting of convex functions in higher dimensions.<br />
<br />
===Tao Mei===<br />
<br />
Fourier Multipliers on free groups.<br />
<br />
In this introductory talk, I will try to explain what is the noncommutative Lp spaces associated with the free groups, and what are the to be answered questions on the corresponding Fourier multiplier operators. At the end, I will explain a recent work on an analogue of Mikhlin’s Lp Fourier multiplier theory on free groups (joint with Eric Ricard and Quanhua Xu).<br />
<br />
=[[Previous_Analysis_seminars]]=<br />
<br />
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars<br />
<br />
=Extras=<br />
<br />
[[Blank Analysis Seminar Template]]<br />
<br />
<br />
Graduate Student Seminar:<br />
<br />
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22566Colloquia2022-01-25T23:31:03Z<p>Gong: /* April 15, 2022, Bernhard Lamel, (Texas A&M University at Qatar) */</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 />
(local)<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 />
== 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>Gonghttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22565Colloquia2022-01-25T23:28:34Z<p>Gong: /* April 15, 2022, Bernhard Lamel[https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-lamel], (Texas A&M University at Qatar) */</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 />
(local)<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, 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 />
== 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>Gonghttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22564Colloquia2022-01-25T23:25:43Z<p>Gong: /* April 15, 2022, Bernhard Lamel, (Texas A&M University at Qatar) */</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 />
(local)<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, Bernhard Lamel[https://www.qatar.tamu.edu/programs/science/faculty-and-staff/berhand-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 />
== 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>Gonghttps://wiki.math.wisc.edu/index.php?title=Colloquia&diff=22563Colloquia2022-01-25T23:21:08Z<p>Gong: /* April 15, 2022, RESERVED, (TBA) */</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 />
(local)<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, 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 />
== 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>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=22326Analysis Seminar2021-12-07T23:43:47Z<p>Gong: </p>
<hr />
<div><br />
The 2021-2022 Analysis Seminar will be organized by David Beltran and Andreas Seeger.<br />
Some of the talks will be in person (room Van Vleck B139) and some will be online. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).<br />
<br />
Zoom links will be sent to those who have signed up for the Analysis Seminar List. 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. If you are from an institution different than UW-Madison, please send as well as an additional email to David and Andreas (dbeltran, seeger at math (dot) wisc (dot) edu) to notify the request.<br />
<br />
If you'd like to suggest speakers for the fall semester please contact David and Andreas.<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 21, VV B139<br />
| Dóminique Kemp<br />
| UW-Madison<br />
|[[#Dóminique Kemp | Decoupling by way of approximation ]]<br />
| <br />
|-<br />
|September 28, VV B139<br />
| Jack Burkart<br />
| UW-Madison<br />
|[[#Jack Burkart | Transcendental Julia Sets with Fractional Packing Dimension ]]<br />
| <br />
|-<br />
|October 5, Online<br />
| Giuseppe Negro<br />
| University of Birmingham<br />
|[[#Giuseppe Negro | Stability of sharp Fourier restriction to spheres ]]<br />
| <br />
|-<br />
|October 12, VV B139<br />
|Rajula Srivastava<br />
|UW Madison<br />
|[[#Rajula Srivastava | Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups ]]<br />
| <br />
|-<br />
|October 19, Online<br />
|Itamar Oliveira<br />
|Cornell University <br />
|[[#Itamar Oliveira | A new approach to the Fourier extension problem for the paraboloid ]]<br />
| <br />
|-<br />
|October 26, VV B139<br />
| Changkeun Oh<br />
| UW Madison<br />
|[[#Changkeun Oh | Decoupling inequalities for quadratic forms and beyond ]]<br />
| <br />
|-<br />
|October 29, Colloquium<br />
| Alexandru Ionescu <br />
| Princeton University<br />
|[[#Alexandru Ionescu | Polynomial averages and pointwise ergodic theorems on nilpotent groups]]<br />
|-<br />
|November 2, VV B139<br />
| Liding Yao<br />
| UW Madison<br />
|[[#Liding Yao | An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains ]]<br />
| <br />
|-<br />
|November 9, VV B139<br />
| Lingxiao Zhang<br />
| UW Madison<br />
|[[#Lingxiao Zhang | Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition ]]<br />
| <br />
|-<br />
|November 12, Colloquium<br />
| Kasso Okoudjou <br />
| Tufts University<br />
|[[#Kasso Okoudjou | An exploration in analysis on fractals ]]<br />
|-<br />
|November 16, VV B139<br />
| Rahul Parhi<br />
| UW Madison (EE)<br />
|[[#Rahul Parhi | On BV Spaces, Splines, and Neural Networks ]]<br />
| <br />
|-<br />
|November 30, VV B139<br />
| Alexei Poltoratski<br />
| UW Madison<br />
|[[#Alexei Poltoratski | Pointwise convergence for the scattering data and non-linear Fourier transform. ]]<br />
| <br />
|-<br />
|December 7, Online<br />
| John Green<br />
| The University of Edinburgh<br />
|[[#John Green | Estimates for oscillatory integrals via sublevel set estimates ]]<br />
| <br />
|-<br />
|December 14, VV B139<br />
| Tao Mei<br />
| Baylor University<br />
|[[#Tao Mei | Fourier Multipliers on free groups ]]<br />
| <br />
|-<br />
|February 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|February 15<br />
| Sebastian Bechtel<br />
| Institut de Mathématiques de Bordeaux<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|February 22<br />
|Betsy Stovall <br />
|UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 8<br />
| Brian Street<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 15: No Seminar<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 22<br />
| Laurent Stolovitch<br />
| University of Cote d'Azur<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 30<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 5<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 19<br />
| No seminar<br />
| <br />
|<br />
| <br />
|-<br />
|April 22, Colloquium<br />
|Detlef Müller<br />
|University of Kiel<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 25, 4:00 p.m., Distinguished Lecture Series <br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 26, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 27, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|Talks in the Fall semester 2022: <br />
|-<br />
|September 20, PDE and Analysis Seminar<br />
|Andrej Zlatoš<br />
|UCSD<br />
|[[#linktoabstract | Title ]]<br />
| Hung Tran<br />
|-<br />
<br />
<br />
|}<br />
<br />
=Abstracts=<br />
===Dóminique Kemp===<br />
<br />
Decoupling by way of approximation<br />
<br />
Since Bourgain and Demeter's seminal 2017 decoupling result for nondegenerate hypersurfaces, several attempts have been made to extend the theory to degenerate hypersurfaces $M$. In this talk, we will discuss using surfaces derived from the local Taylor expansions of $M$ in order to obtain "approximate" decoupling results. By themselves, these approximate decouplings do not avail much. However, upon considerate iteration, for a specifically chosen $M$, they culminate in a decoupling partition of $M$ into caps small enough either as originally desired or otherwise genuinely nondegenerate at the local scale. A key feature that will be discussed is the notion of approximating a non-convex hypersurface $M$ by convex hypersurfaces at various scales. In this manner, contrary to initial intuition, non-trivial $\ell^2$ decoupling results will be obtained for $M$.<br />
<br />
===Jack Burkart===<br />
<br />
Transcendental Julia Sets with Fractional Packing Dimension<br />
<br />
If f is an entire function, the Julia set of f is the set of all points such that f and its iterates locally do not form a normal family; nearby points have very different orbits under iteration by f. A topic of interest in complex dynamics is studying the fractal geometry of the Julia set.<br />
<br />
In this talk, we will discuss my thesis result where I construct non-polynomial (transcendental) entire functions whose Julia set has packing dimension strictly between (1,2). We will introduce various notions of dimension and basic objects in complex dynamics, and discuss a history of dimension results in complex dynamics. We will discuss some key aspects of the proof, which include a use of Whitney decompositions of domains as a tool to calculate the packing dimension, and some open questions I am thinking about.<br />
<br />
===Giuseppe Negro===<br />
<br />
Stability of sharp Fourier restriction to spheres<br />
<br />
In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate. <br />
<br />
Joint work with E.Carneiro and D.Oliveira e Silva.<br />
<br />
===Rajula Srivastava===<br />
<br />
Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups<br />
<br />
We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.<br />
<br />
===Itamar Oliveira===<br />
<br />
A new approach to the Fourier extension problem for the paraboloid<br />
<br />
An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $ of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.<br />
<br />
===Changkeun Oh===<br />
<br />
Decoupling inequalities for quadratic forms and beyond<br />
<br />
In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.<br />
<br />
===Alexandru Ionescu===<br />
<br />
Polynomial averages and pointwise ergodic theorems on nilpotent groups<br />
<br />
I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.<br />
<br />
===Liding Yao===<br />
<br />
An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains<br />
<br />
Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.<br />
<br />
===Lingxiao Zhang===<br />
<br />
Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition<br />
<br />
We study operators of the form<br />
$Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$ <br />
where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.<br />
<br />
===Kasso Okoudjou===<br />
<br />
An exploration in analysis on fractals<br />
<br />
Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.<br />
<br />
===Rahul Parhi===<br />
<br />
On BV Spaces, Splines, and Neural Networks<br />
<br />
Many problems in science and engineering can be phrased as the problem<br />
of reconstructing a function from a finite number of possibly noisy<br />
measurements. The reconstruction problem is inherently ill-posed when<br />
the allowable functions belong to an infinite set. Classical techniques<br />
to solve this problem assume, a priori, that the underlying function has<br />
some kind of regularity, typically Sobolev, Besov, or BV regularity. The<br />
field of applied harmonic analysis is interested in studying efficient<br />
decompositions and representations for functions with certain<br />
regularity. Common representation systems are based on splines and<br />
wavelets. These are well understood mathematically and have been<br />
successfully applied in a variety of signal processing and statistical<br />
tasks. Neural networks are another type of representation system that is<br />
useful in practice, but poorly understood mathematically.<br />
<br />
In this talk, I will discuss my research which aims to rectify this<br />
issue by understanding the regularity properties of neural networks in a<br />
similar vein to classical methods based on splines and wavelets. In<br />
particular, we will show that neural networks are optimal solutions to<br />
variational problems over BV-type function spaces defined via the Radon<br />
transform. These spaces are non-reflexive Banach spaces, generally<br />
distinct from classical spaces studied in analysis. However, in the<br />
univariate setting, neural networks reduce to splines and these function<br />
spaces reduce to classical univariate BV spaces. If time permits, I will<br />
also discuss approximation properties of these spaces, showing that they<br />
are, in some sense, "small" compared to classical multivariate spaces<br />
such as Sobolev or Besov spaces.<br />
<br />
This is joint work with Robert Nowak.<br />
<br />
===Alexei Poltoratski===<br />
<br />
Title: Pointwise convergence for the scattering data and non-linear Fourier transform.<br />
<br />
Abstract: This talk is about applications of complex and harmonic analysis in spectral and scattering theory<br />
for differential operators. The scattering transform for the Dirac system of differential equations<br />
can be viewed as the non-linear version of the classical Fourier transform. This connection raises many natural<br />
problems on extensions of classical results of Fourier analysis to non-linear settings. In this talk<br />
I will discuss one of such problems, an extension of Carleson's theorem on pointwise convergence of Fourier series to the non-linear case.<br />
<br />
<br />
<br />
===John Green===<br />
<br />
Estimates for oscillatory integrals via sublevel set estimates.<br />
<br />
In many situations, oscillatory integral estimates are known to imply sublevel set estimates in a stable manner. Reversing this implication is much more difficult, but understanding when this is true is helpful for understanding scalar oscillatory integral estimates. We shall motivate a line of investigation in which we seek to reverse the implication in the presence of a qualitative structural assumption. After considering some one-dimensional results, we turn to the setting of convex functions in higher dimensions.<br />
<br />
===Tao Mei===<br />
<br />
Fourier Multipliers on free groups.<br />
<br />
In this introductory talk, I will try to explain what is the noncommutative Lp spaces associated with the free groups, and what are the to be answered questions on the corresponding Fourier multiplier operators. At the end, I will explain a recent work on an analogue of Mikhlin’s Lp Fourier multiplier theory on free groups (joint with Eric Ricard and Quanhua Xu).<br />
<br />
=[[Previous_Analysis_seminars]]=<br />
<br />
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars<br />
<br />
=Extras=<br />
<br />
[[Blank Analysis Seminar Template]]<br />
<br />
<br />
Graduate Student Seminar:<br />
<br />
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=22325Analysis Seminar2021-12-07T22:59:29Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div><br />
The 2021-2022 Analysis Seminar will be organized by David Beltran and Andreas Seeger.<br />
Some of the talks will be in person (room Van Vleck B139) and some will be online. The regular time for the Seminar will be Tuesdays at 4:00 p.m. (in some cases we will schedule the seminar at different times, to accommodate speakers).<br />
<br />
Zoom links will be sent to those who have signed up for the Analysis Seminar List. 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. If you are from an institution different than UW-Madison, please send as well as an additional email to David and Andreas (dbeltran, seeger at math (dot) wisc (dot) edu) to notify the request.<br />
<br />
If you'd like to suggest speakers for the fall semester please contact David and Andreas.<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|September 21, VV B139<br />
| Dóminique Kemp<br />
| UW-Madison<br />
|[[#Dóminique Kemp | Decoupling by way of approximation ]]<br />
| <br />
|-<br />
|September 28, VV B139<br />
| Jack Burkart<br />
| UW-Madison<br />
|[[#Jack Burkart | Transcendental Julia Sets with Fractional Packing Dimension ]]<br />
| <br />
|-<br />
|October 5, Online<br />
| Giuseppe Negro<br />
| University of Birmingham<br />
|[[#Giuseppe Negro | Stability of sharp Fourier restriction to spheres ]]<br />
| <br />
|-<br />
|October 12, VV B139<br />
|Rajula Srivastava<br />
|UW Madison<br />
|[[#Rajula Srivastava | Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups ]]<br />
| <br />
|-<br />
|October 19, Online<br />
|Itamar Oliveira<br />
|Cornell University <br />
|[[#Itamar Oliveira | A new approach to the Fourier extension problem for the paraboloid ]]<br />
| <br />
|-<br />
|October 26, VV B139<br />
| Changkeun Oh<br />
| UW Madison<br />
|[[#Changkeun Oh | Decoupling inequalities for quadratic forms and beyond ]]<br />
| <br />
|-<br />
|October 29, Colloquium<br />
| Alexandru Ionescu <br />
| Princeton University<br />
|[[#Alexandru Ionescu | Polynomial averages and pointwise ergodic theorems on nilpotent groups]]<br />
|-<br />
|November 2, VV B139<br />
| Liding Yao<br />
| UW Madison<br />
|[[#Liding Yao | An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains ]]<br />
| <br />
|-<br />
|November 9, VV B139<br />
| Lingxiao Zhang<br />
| UW Madison<br />
|[[#Lingxiao Zhang | Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition ]]<br />
| <br />
|-<br />
|November 12, Colloquium<br />
| Kasso Okoudjou <br />
| Tufts University<br />
|[[#Kasso Okoudjou | An exploration in analysis on fractals ]]<br />
|-<br />
|November 16, VV B139<br />
| Rahul Parhi<br />
| UW Madison (EE)<br />
|[[#Rahul Parhi | On BV Spaces, Splines, and Neural Networks ]]<br />
| <br />
|-<br />
|November 30, VV B139<br />
| Alexei Poltoratski<br />
| UW Madison<br />
|[[#Alexei Poltoratski | Pointwise convergence for the scattering data and non-linear Fourier transform. ]]<br />
| <br />
|-<br />
|December 7, Online<br />
| John Green<br />
| The University of Edinburgh<br />
|[[#John Green | Estimates for oscillatory integrals via sublevel set estimates ]]<br />
| <br />
|-<br />
|December 14, VV B139<br />
| Tao Mei<br />
| Baylor University<br />
|[[#Tao Mei | Fourier Multipliers on free groups ]]<br />
| <br />
|-<br />
|February 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|February 15<br />
| Sebastian Bechtel<br />
| Institut de Mathématiques de Bordeaux<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|February 22<br />
|Betsy Stovall <br />
|UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 8<br />
| Brian Street<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 15: No Seminar<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 23<br />
| Laurent Stolovitch<br />
| University of Cote d'Azur<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|March 30<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 5<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 19<br />
| No seminar<br />
| <br />
|<br />
| <br />
|-<br />
|April 22, Colloquium<br />
|Detlef Müller<br />
|University of Kiel<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|April 25, 4:00 p.m., Distinguished Lecture Series <br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 26, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
|-<br />
|April 27, 4:00 p.m., Distinguished Lecture Series<br />
|Larry Guth <br />
|MIT<br />
|[[#linktoabstract | Title ]]<br />
| <br />
|-<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
|Talks in the Fall semester 2022: <br />
|-<br />
|September 20, PDE and Analysis Seminar<br />
|Andrej Zlatoš<br />
|UCSD<br />
|[[#linktoabstract | Title ]]<br />
| Hung Tran<br />
|-<br />
<br />
<br />
|}<br />
<br />
=Abstracts=<br />
===Dóminique Kemp===<br />
<br />
Decoupling by way of approximation<br />
<br />
Since Bourgain and Demeter's seminal 2017 decoupling result for nondegenerate hypersurfaces, several attempts have been made to extend the theory to degenerate hypersurfaces $M$. In this talk, we will discuss using surfaces derived from the local Taylor expansions of $M$ in order to obtain "approximate" decoupling results. By themselves, these approximate decouplings do not avail much. However, upon considerate iteration, for a specifically chosen $M$, they culminate in a decoupling partition of $M$ into caps small enough either as originally desired or otherwise genuinely nondegenerate at the local scale. A key feature that will be discussed is the notion of approximating a non-convex hypersurface $M$ by convex hypersurfaces at various scales. In this manner, contrary to initial intuition, non-trivial $\ell^2$ decoupling results will be obtained for $M$.<br />
<br />
===Jack Burkart===<br />
<br />
Transcendental Julia Sets with Fractional Packing Dimension<br />
<br />
If f is an entire function, the Julia set of f is the set of all points such that f and its iterates locally do not form a normal family; nearby points have very different orbits under iteration by f. A topic of interest in complex dynamics is studying the fractal geometry of the Julia set.<br />
<br />
In this talk, we will discuss my thesis result where I construct non-polynomial (transcendental) entire functions whose Julia set has packing dimension strictly between (1,2). We will introduce various notions of dimension and basic objects in complex dynamics, and discuss a history of dimension results in complex dynamics. We will discuss some key aspects of the proof, which include a use of Whitney decompositions of domains as a tool to calculate the packing dimension, and some open questions I am thinking about.<br />
<br />
===Giuseppe Negro===<br />
<br />
Stability of sharp Fourier restriction to spheres<br />
<br />
In dimension $d\in\{3, 4, 5, 6, 7\}$, we establish that the constant functions maximize the weighted $L^2(S^{d-1}) - L^4(R^d)$ Fourier extension estimate on the sphere, provided that the weight function is sufficiently regular and small, in a proper and effective sense which we will make precise. One of the main tools is an integration by parts identity, which generalizes the so-called "magic identity" of Foschi for the unweighted inequality with $d=3$, which is exactly the classical Stein-Tomas estimate. <br />
<br />
Joint work with E.Carneiro and D.Oliveira e Silva.<br />
<br />
===Rajula Srivastava===<br />
<br />
Lebesgue space estimates for Spherical Maximal Functions on Heisenberg groups<br />
<br />
We discuss $L^p\to L^q$ estimates for local maximal operators associated with dilates of codimension two spheres in Heisenberg groups, sharp up to endpoints. The proof shall be reduced to estimates for standard oscillatory integrals of Carleson-Sj\"olin-H\"ormander type, relying on the maximal possible number of nonvanishing curvatures for a cone in the fibers of the associated canonical relation. We shall also discuss a new counterexample which shows the sharpness of one of the edges in the region of boundedness. Based on joint work with Joris Roos and Andreas Seeger.<br />
<br />
===Itamar Oliveira===<br />
<br />
A new approach to the Fourier extension problem for the paraboloid<br />
<br />
An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps $ L^{2+\frac{2}{d}}([0,1]^{d}) $ to $L^{2+\frac{2}{d}+\varepsilon}(\mathbb{R}^{d+1}) $ for every $\varepsilon>0 $. It has been fully solved only for $ d=1 $ and there are many partial results in higher dimensions regarding the range of $ (p,q) $ for which $L^{p}([0,1]^{d}) $ is mapped to $ L^{q}(\mathbb{R}^{d+1}) $. One can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all $ g $ of the form $ g(x_{1},\ldots,x_{d})=g_{1}(x_{1})\cdot\ldots\cdot g_{d}(x_{d}) $. We will present this theorem as a proof of concept of a more general framework and set of techniques that can also address multilinear versions of this problem and get similar results. This is joint work with Camil Muscalu.<br />
<br />
===Changkeun Oh===<br />
<br />
Decoupling inequalities for quadratic forms and beyond<br />
<br />
In this talk, I will present some recent progress on decoupling inequalities for some translation- and dilation-invariant systems (TDI systems in short). In particular, I will emphasize decoupling inequalities for quadratic forms. If time permits, I will also discuss some interesting phenomenon related to Brascamp-Lieb inequalities that appears in the study of a cubic TDI system. Joint work with Shaoming Guo, Pavel Zorin-Kranich, and Ruixiang Zhang.<br />
<br />
===Alexandru Ionescu===<br />
<br />
Polynomial averages and pointwise ergodic theorems on nilpotent groups<br />
<br />
I will talk about some recent work on pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two. Our proof is based on almost-orthogonality techniques that go far beyond Fourier transform tools, which are not available in the non-commutative nilpotent setting. In particular we develop what we call a nilpotent circle method}, which allows us to adapt some the ideas of the classical circle method to the setting of nilpotent groups.<br />
<br />
===Liding Yao===<br />
<br />
An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains<br />
<br />
Given a bounded Lipschitz domain $\Omega\subset\mathbb{R}^n$, Rychkov showed that there is a linear extension operator $\mathcal E$ for $\Omega$ which is bounded in Besov and Triebel-Lizorkin spaces. We introduce a class of operators that generalize $\mathcal E$ which are more versatile for applications. We also derive some quantitative blow-up estimates of the extended function and all its derivatives in $\overline{\Omega}^c$ up to boundary. This is a joint work with Ziming Shi.<br />
<br />
===Lingxiao Zhang===<br />
<br />
Real Analytic Multi-parameter Singular Radon Transforms: necessity of the Stein-Street condition<br />
<br />
We study operators of the form<br />
$Tf(x)= \psi(x) \int f(\gamma_t(x))K(t)\,dt$ <br />
where $\gamma_t(x)$ is a real analytic function of $(t,x)$ mapping from a neighborhood of $(0,0)$ in $\mathbb{R}^N \times \mathbb{R}^n$ into $\mathbb{R}^n$ satisfying $\gamma_0(x)\equiv x$, $\psi(x) \in C_c^\infty(\mathbb{R}^n)$, and $K(t)$ is a `multi-parameter singular kernel' with compact support in $\mathbb{R}^N$; for example when $K(t)$ is a product singular kernel. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth $\gamma_t(x)$, in the single-parameter case when $K(t)$ is a Calder\'on-Zygmund kernel. Street and Stein generalized their work to the multi-parameter case, and gave sufficient conditions for the $L^p$-boundedness of such operators. This paper shows that when $\gamma_t(x)$ is real analytic, the sufficient conditions of Street and Stein are also necessary for the $L^p$-boundedness of $T$, for all such kernels $K$.<br />
<br />
===Kasso Okoudjou===<br />
<br />
An exploration in analysis on fractals<br />
<br />
Analysis on fractal sets such as the Sierpinski gasket is based on the spectral analysis of a corresponding Laplace operator. In the first part of the talk, I will describe a class of fractals and the analytical tools that they support. In the second part of the talk, I will consider fractal analogs of topics from classical analysis, including the Heisenberg uncertainty principle, the spectral theory of Schrödinger operators, and the theory of orthogonal polynomials.<br />
<br />
===Rahul Parhi===<br />
<br />
On BV Spaces, Splines, and Neural Networks<br />
<br />
Many problems in science and engineering can be phrased as the problem<br />
of reconstructing a function from a finite number of possibly noisy<br />
measurements. The reconstruction problem is inherently ill-posed when<br />
the allowable functions belong to an infinite set. Classical techniques<br />
to solve this problem assume, a priori, that the underlying function has<br />
some kind of regularity, typically Sobolev, Besov, or BV regularity. The<br />
field of applied harmonic analysis is interested in studying efficient<br />
decompositions and representations for functions with certain<br />
regularity. Common representation systems are based on splines and<br />
wavelets. These are well understood mathematically and have been<br />
successfully applied in a variety of signal processing and statistical<br />
tasks. Neural networks are another type of representation system that is<br />
useful in practice, but poorly understood mathematically.<br />
<br />
In this talk, I will discuss my research which aims to rectify this<br />
issue by understanding the regularity properties of neural networks in a<br />
similar vein to classical methods based on splines and wavelets. In<br />
particular, we will show that neural networks are optimal solutions to<br />
variational problems over BV-type function spaces defined via the Radon<br />
transform. These spaces are non-reflexive Banach spaces, generally<br />
distinct from classical spaces studied in analysis. However, in the<br />
univariate setting, neural networks reduce to splines and these function<br />
spaces reduce to classical univariate BV spaces. If time permits, I will<br />
also discuss approximation properties of these spaces, showing that they<br />
are, in some sense, "small" compared to classical multivariate spaces<br />
such as Sobolev or Besov spaces.<br />
<br />
This is joint work with Robert Nowak.<br />
<br />
===Alexei Poltoratski===<br />
<br />
Title: Pointwise convergence for the scattering data and non-linear Fourier transform.<br />
<br />
Abstract: This talk is about applications of complex and harmonic analysis in spectral and scattering theory<br />
for differential operators. The scattering transform for the Dirac system of differential equations<br />
can be viewed as the non-linear version of the classical Fourier transform. This connection raises many natural<br />
problems on extensions of classical results of Fourier analysis to non-linear settings. In this talk<br />
I will discuss one of such problems, an extension of Carleson's theorem on pointwise convergence of Fourier series to the non-linear case.<br />
<br />
<br />
<br />
===John Green===<br />
<br />
Estimates for oscillatory integrals via sublevel set estimates.<br />
<br />
In many situations, oscillatory integral estimates are known to imply sublevel set estimates in a stable manner. Reversing this implication is much more difficult, but understanding when this is true is helpful for understanding scalar oscillatory integral estimates. We shall motivate a line of investigation in which we seek to reverse the implication in the presence of a qualitative structural assumption. After considering some one-dimensional results, we turn to the setting of convex functions in higher dimensions.<br />
<br />
===Tao Mei===<br />
<br />
Fourier Multipliers on free groups.<br />
<br />
In this introductory talk, I will try to explain what is the noncommutative Lp spaces associated with the free groups, and what are the to be answered questions on the corresponding Fourier multiplier operators. At the end, I will explain a recent work on an analogue of Mikhlin’s Lp Fourier multiplier theory on free groups (joint with Eric Ricard and Quanhua Xu).<br />
<br />
=[[Previous_Analysis_seminars]]=<br />
<br />
https://www.math.wisc.edu/wiki/index.php/Previous_Analysis_seminars<br />
<br />
=Extras=<br />
<br />
[[Blank Analysis Seminar Template]]<br />
<br />
<br />
Graduate Student Seminar:<br />
<br />
https://www.math.wisc.edu/~sguo223/2020Fall_graduate_seminar.html</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=19219Analysis Seminar2020-03-07T01:21:07Z<p>Gong: </p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wick<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Purdue University Fort Wayne<br />
|[[#linktoabstract |On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Isometries of Wasserstein spaces ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
<br />
===Tamás Titkos===<br />
<br />
<b>Isometries of Wasserstein spaces</b><br />
<br />
Due to its nice theoretical properties and an astonishing number of applications via optimal transport problems, probably the most intensively studied metric nowadays is the $p$-Wasserstein metric. Given a complete and separable metric space $X$ and a real number $p\geq1$, one defines the $p$-Wasserstein space $\mathcal{W}_p(X)$ as the collection of Borel probability measures with finite $p$-th moment, endowed with a distance which is calculated by means of transport plans.<br />
<br />
The main aim of our research project is to reveal the structure of the isometry group $\mathrm{Isom}(\mathcal{W}_p(X))$. Although $\mathrm{Isom}(X)$ embeds naturally into $\mathrm{Isom}(\mathcal{W}_p(X))$ by push-forward, and this embedding turned out to be surjective in many cases, these two groups are not isomorphic in general. Recently, Kloeckner described the isometry group of the quadratic Wasserstein space over the real line. It turned out that this group is extremely rich: it contains a flow of wild behaving isometries that distort the shape of measures. Following this line of investigation, we described $\mathrm{Isom}(\mathcal{W}_p(\mathbb{R}))$ and $\mathrm{Isom}(\mathcal{W}_p([0,1])$ for all $p\geq 1$. In this talk I will survey first some of the earlier results in the subject, and then I will present the key results of our recent manuscript \emph{"Isometric study of Wasserstein spaces -- The real line"} (to appear in Trans. Amer. Math. Soc., arXiv:2002.00859).<br />
<br />
Joint work with György Pál Gehér (University of Reading) and Dániel Virosztek (IST Austria).<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=19217Analysis Seminar2020-03-07T01:06:08Z<p>Gong: </p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Brian<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Brian<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| UW Madison<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Sergey<br />
|-<br />
|Friday, Feb 28 (Colloquium)<br />
| Brett Wick<br />
| Washington University - St. Louis<br />
|[[#MBrett Wick | The Corona Theorem]]<br />
| Andreas<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Purdue University Fort Wayne<br />
|[[#linktoabstract |(talk canceled) On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Isometries of Wasserstein spaces ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
<br />
===Tamás Titkos===<br />
<br />
<b>Isometries of Wasserstein spaces</b><br />
<br />
Due to its nice theoretical properties and an astonishing number of applications via optimal transport problems, probably the most intensively studied metric nowadays is the $p$-Wasserstein metric. Given a complete and separable metric space $X$ and a real number $p\geq1$, one defines the $p$-Wasserstein space $\mathcal{W}_p(X)$ as the collection of Borel probability measures with finite $p$-th moment, endowed with a distance which is calculated by means of transport plans.<br />
<br />
The main aim of our research project is to reveal the structure of the isometry group $\mathrm{Isom}(\mathcal{W}_p(X))$. Although $\mathrm{Isom}(X)$ embeds naturally into $\mathrm{Isom}(\mathcal{W}_p(X))$ by push-forward, and this embedding turned out to be surjective in many cases, these two groups are not isomorphic in general. Recently, Kloeckner described the isometry group of the quadratic Wasserstein space over the real line. It turned out that this group is extremely rich: it contains a flow of wild behaving isometries that distort the shape of measures. Following this line of investigation, we described $\mathrm{Isom}(\mathcal{W}_p(\mathbb{R}))$ and $\mathrm{Isom}(\mathcal{W}_p([0,1])$ for all $p\geq 1$. In this talk I will survey first some of the earlier results in the subject, and then I will present the key results of our recent manuscript \emph{"Isometric study of Wasserstein spaces -- The real line"} (to appear in Trans. Amer. Math. Soc., arXiv:2002.00859).<br />
<br />
Joint work with György Pál Gehér (University of Reading) and Dániel Virosztek (IST Austria).<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=19159Analysis Seminar2020-02-26T16:44:39Z<p>Gong: </p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| Local<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Denisov<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Purdue University Fort Wayne<br />
|[[#linktoabstract | On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b>On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n</b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=19158Analysis Seminar2020-02-26T16:42:56Z<p>Gong: </p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#Bingyang Hu | Sparse bounds of singular Radon transforms]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#Francesco di Plinio | Maximal directional integrals along algebraic and lacunary sets]]<br />
| Shaoming<br />
|-<br />
|Nov 13 (Wednesday)<br />
| Xiaochun Li <br />
| UIUC<br />
|[[#Xiaochun Li | Roth's type theorems on progressions]]<br />
| Brian, Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#Joao Ramos | Fourier uncertainty principles, interpolation and uniqueness sets ]]<br />
| Joris, Shaoming<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Friday, Jan 31, 4 pm, B239, Colloquium<br />
| Lillian Pierce<br />
| Duke University<br />
|[[#Lillian Pierce | On Bourgain’s counterexample for the Schrödinger maximal function ]]<br />
| Andreas, Simon<br />
|-<br />
|Feb 4<br />
| Ruixiang Zhang<br />
| UW Madison<br />
|[[#Ruixiang Zhang | Local smoothing for the wave equation in 2+1 dimensions ]]<br />
| Andreas<br />
|-<br />
|Feb 11<br />
| Zane Li<br />
| Indiana University<br />
|[[#Zane Li | A bilinear proof of decoupling for the moment curve ]]<br />
| Betsy<br />
|-<br />
|Feb 18<br />
| Sergey Denisov<br />
| UW Madison<br />
|[[#linktoabstract | De Branges canonical systems with finite logarithmic integral ]]<br />
| Street<br />
|-<br />
|Feb 25<br />
| Michel Alexis<br />
| Local<br />
|[[#Michel Alexis | The Steklov problem for trigonometric polynomials orthogonal to a Muckenhoupt weight ]]<br />
| Denisov<br />
|-<br />
|Mar 3<br />
| William Green<br />
| Rose-Hulman Institute of Technology<br />
|[[#William Green | Dispersive estimates for the Dirac equation ]]<br />
| Betsy<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Purdue University Fort Wayne<br />
|[[#linktoabstract | On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Brian Street<br />
| University of Wisconsin-Madison<br />
|[[#linktoabstract | Title ]]<br />
| Local<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|<b>Monday, Apr 13</b><br />
|Yumeng Ou<br />
|CUNY, Baruch College<br />
|[[#linktoabstract | TBA ]]<br />
|Zhang<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
<br />
<br />
===Joao Ramos===<br />
<br />
Title: Fourier uncertainty principles, interpolation and uniqueness sets<br />
<br />
Abstract: A classical result in the theory of entire functions of exponential type, Shannon’s interpolation formula predicates that, given a function whose Fourier transform vanishes outside the interval $[-1/2,1/2]$, it is possible to recover it from its values at the integers. More specifically, it holds, in a suitable sense of convergence, that <br />
<br />
$$ f(x) = \sum_{n \in \mathbb{Z}} f(n) \frac{\sin(\pi(x-n))}{\pi(x -n)}. $$ <br />
<br />
This formula is unfortunately unavailable for arbitrary Schwartz functions on the real line, but a recent result of Radchenko and Viazovska provides us with an explicit construction of an interpolation basis for even Schwartz functions. It states, in a nutshell, that we can recover explicitly the function given its values at the squares of roots of integers. <br />
<br />
We will discuss a bit these two results, and explore, in connection to classical Fourier uncertainty results, the question of determining which pairs of sets $(A,B)$ satisfy that, if a Schwartz function $f$ vanishes on A and its Fourier transform vanishes on B, then $f \equiv 0.$ <br />
<br />
In particular, we will give sufficient conditions on $(\alpha,\beta)$ pairs of positive numbers so that, if $f$ vanishes at $\pm n^{\alpha}$ and its Fourier transform vanishes at $\pm n^{\beta}$, then $f$ is identically zero.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
<br />
===Xiaochun Li===<br />
<br />
Title: Roth’s type theorems on progressions<br />
<br />
Abstract: The arithmetic progression problems were posed by Erd\”os-Turan, answered affirmatively by Semer\’edi. However, there are still many questions remained on precise quantitative description on how large a subset shall be in oredr to guarantee a progression in it. Involving with Fourier analysis, considerable work had been accomplished recently. We will give a survey on those progress, and report our recent progress on quantitative version of Roth’s type theorem on (polynomial) progressions of short length.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Francesco di Plinio===<br />
<br />
<b>Maximal directional integrals along algebraic and lacunary sets </b><br />
<br />
I will discuss two recent results obtained in collaboration with (partly) Natalia Accomazzo and Ioannis Parissis (U Basque Country). The first is a sharp $L^2$ estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth. The second result is a sharp estimate in all dimensions for the maximal directional singular integrals along lacunary directions. This settles a question of Parcet and Rogers. The proof uses a combination of two-dimensional and $n$-dimensional coverings combining seemingly contrasting ideas of Parcet-Rogers and of Nagel-Stein-Wainger.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
===Bingyang Hu===<br />
<br />
<b>Sparse bounds of singular Radon transforms</b><br />
<br />
In this talk, we will first briefly talk about the general theory of sparse domination, and then talk about the sparse bounds of singular Radon transforms, which strengths the $L^p$ boundedness of such operators due to Christ, Nagel, Stein and Wainger in 1999.<br />
<br />
===Lillian Pierce===<br />
<b> On Bourgain’s counterexample for the Schrödinger maximal function </b><br />
<br />
In 1980, Carleson asked a question in harmonic analysis: to which Sobolev space H^s must an initial data function belong, for a pointwise a.e. convergence result to hold for the solution to the associated linear Schrödinger equation? Over the next decades, many people developed counterexamples to push the (necessary) range of s up, and positive results to push the (sufficient) range of s down. Now, these ranges are finally meeting: Bourgain’s 2016 counterexample showed s < n/(2(n+1)) fails, and Du and Zhang’s 2019 paper shows that s>n/(2(n+1)) suffices. <br />
In this talk, we will give an overview of how to rigorously derive Bourgain’s 2016 counterexample, based on simple facts from number theory. We will show how to build Bourgain’s counterexample starting from “zero knowledge," and how to gradually optimize the set-up to arrive at the final counterexample. The talk will be broadly accessible, particularly if we live up to the claim of starting from “zero knowledge.”<br />
<br />
===Ruixiang Zhang===<br />
<br />
<b> Local smoothing for the wave equation in 2+1 dimensions </b><br />
<br />
Sogge's local smoothing conjecture for the wave equation predicts that the local L^p space-time estimate gains a fractional derivative of order almost 1/p compared to the fixed time L^p estimates, when p>2n/(n-1). Jointly with Larry Guth and Hong Wang, we recently proved the conjecture in $\mathbb{R}^{2+1}$. I will talk about a sharp square function estimate we proved which implies the local smoothing conjecture in dimensions 2+1. A key ingredient in the proof is an incidence type theorem.<br />
<br />
===Zane Li===<br />
<br />
<b> A bilinear proof of decoupling for the moment curve</b><br />
<br />
We give a proof of decoupling for the moment curve that is inspired from nested efficient congruencing. We also discuss the relationship between Wooley's nested efficient congruencing and Bourgain-Demeter-Guth's decoupling proofs of Vinogradov's Mean Value Theorem. This talk is based on joint work with Shaoming Guo, Po-Lam Yung, and Pavel Zorin-Kranich.<br />
<br />
<br />
===Sergey Denisov===<br />
<br />
<b> De Branges canonical systems with finite logarithmic integral </b><br />
<br />
We consider measures m on the real line for which logarithmic<br />
integral exists and give a complete characterization of all Hamiltonians<br />
in de Branges canonical system for which m is the spectral measure.<br />
This characterization involves the matrix A_2 Muckenhoupt condition on a<br />
fixed scale. Our result provides a generalization of the classical<br />
theorem of Szego for polynomials orthogonal on the unit circle and<br />
complements the Krein-Wiener theorem. Based on the joint work with R.<br />
Bessonov.<br />
<br />
<br />
===Michel Alexis===<br />
<br />
<b>The Steklov problem for Trigonometric Polynomials orthogonal to a Muckenhoupt weight</b><br />
<br />
Let $\{\varphi_n\}_{n=0}^{\infty}$ be the sequence of degree $n$ polynomials on $\mathbb{T}$, orthonormal with respect to a positive weight $w$. Steklov conjectured whenever $w \geq \delta> 0$ a.e.\ then $\{\varphi_n\}$ are uniformly bounded in $L^{\infty}$. While false, this conjecture brings us to ask the following: under what regularity conditions on $w$ are $\{\varphi_n\}$ uniformly bounded in $L^p (w)$ for some $p > 2$?<br />
<br />
We discuss some answers to this question using the contraction principle and operator estimates for the Hilbert transform, in particular recent joint work with Alexander Aptakarev and Sergey Denisov for when $w$ is a Muckenhoupt weight.<br />
<br />
===William Green===<br />
<br />
<b> Dispersive estimates for the Dirac equation </b><br />
<br />
The Dirac equation was derived by Dirac in 1928 to model the behavior of subatomic particles moving at relativistic speeds. Dirac formulated a hyberbolic system of partial differential equations<br />
That can be interpreted as a sort of square root of a system of Klein-Gordon equations.<br />
<br />
The Dirac equation is considerably less well studied than other dispersive equations such as the Schrodinger, wave or Klein-Gordon equations. We will survey recent work on time-decay estimates for the solution operator. Specifically the mapping properties of the solution operator between L^p spaces. As in other dispersive equations, the existence of eigenvalues and/or resonances at the edge of the continuous spectrum affects the dynamics of the solution. We classify the threshold eigenvalue and resonance structure in two and three spatial dimensions and study their effect on the time decay. The talk with survey joint works with B. Erdogan (Illinois), M. Goldberg (Cincinnati) and E. Toprak (Rutgers).<br />
<br />
===Yifei Pan===<br />
<br />
<b> On the Sobolev space property of logarithmic modulus of holomorphic functions in C^n </b><br />
<br />
In this talk, I will present a proof of the following Sobolev space property of logarithmic modulus of holomorphic functions in C^n. If f is a holomorphic function on the unit ball B(0,1) in C^n vanishing at the origin (i.e., f(0) = 0) but it is not identically zero, then log |f| ∈ W^{1,p}(B(0, r)) for any p < 2, but log |f| is not in W^{1,2}(B(0, r)) (r < 1). As you may see, this result is rather simple to prove in the complex plane due to the discreteness of zeros of holomorphic functions. In higher dimensions, we are going to apply Hironaka’s resolution of singularity and then Harvey- Polking removable singularity method to prove the existence of weak derivatives of log |f(z)|. This is part of a joint project with Ziming Shi at Madison.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18580Geometry and Topology Seminar 2019-20202019-12-21T17:25:19Z<p>Gong: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18579Geometry and Topology Seminar 2019-20202019-12-21T17:18:44Z<p>Gong: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18578Geometry and Topology Seminar 2019-20202019-12-21T17:16:24Z<p>Gong: Undo revision 18577 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18577Geometry and Topology Seminar 2019-20202019-12-21T17:12:39Z<p>Gong: Undo revision 18576 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18576Geometry and Topology Seminar 2019-20202019-12-21T17:11:19Z<p>Gong: Undo revision 18569 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18575Geometry and Topology Seminar 2019-20202019-12-21T17:10:58Z<p>Gong: Undo revision 18572 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18574Geometry and Topology Seminar 2019-20202019-12-21T17:10:40Z<p>Gong: Undo revision 18569 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18573Geometry and Topology Seminar 2019-20202019-12-21T17:10:19Z<p>Gong: Undo revision 18572 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18572Geometry and Topology Seminar 2019-20202019-12-21T17:09:56Z<p>Gong: Undo revision 18571 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18571Geometry and Topology Seminar 2019-20202019-12-21T17:09:41Z<p>Gong: Undo revision 18570 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18570Geometry and Topology Seminar 2019-20202019-12-21T17:09:18Z<p>Gong: Undo revision 18569 by Gong (talk)</p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18569Geometry and Topology Seminar 2019-20202019-12-21T17:08:05Z<p>Gong: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18568Geometry and Topology Seminar 2019-20202019-12-21T17:07:26Z<p>Gong: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18567Geometry and Topology Seminar 2019-20202019-12-21T16:54:39Z<p>Gong: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
|Feb. 28<br />
| Reserved <br />
| title<br />
|(Gong)<br />
|-<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18566Geometry and Topology Seminar 2019-20202019-12-21T16:54:00Z<p>Gong: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
|}<br />
<br />
|-<br />
|Feb. 28<br />
| Reserved <br />
| title<br />
|(Gong)<br />
|-<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Geometry_and_Topology_Seminar_2019-2020&diff=18565Geometry and Topology Seminar 2019-20202019-12-21T16:53:26Z<p>Gong: </p>
<hr />
<div>The [[Geometry and Topology]] seminar meets in room '''901 of Van Vleck Hall''' on '''Fridays''' from '''1:20pm - 2:10pm'''.<br />
<br> <br />
For more information, contact Shaosai Huang.<br />
<br />
[[Image:Hawk.jpg|thumb|300px]]<br />
<br />
<br />
== Spring 2020 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Feb. 7<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 1<br />
|(Dymarz)<br />
|-<br />
|Feb. 14<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 2<br />
|(Dymarz)<br />
|-<br />
|Feb. 21<br />
|Xiangdong Xie (Bowling Green University)<br />
| Minicourse 3<br />
|(Dymarz)<br />
|-<br />
|}<br />
<br />
|-<br />
|Feb. 28<br />
| Reserved <br />
| <br />
|(Gong)<br />
|-<br />
|}<br />
<br />
== Fall 2019 ==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date<br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Oct. 4<br />
|Ruobing Zhang (Stony Brook University)<br />
| Geometric analysis of collapsing Calabi-Yau spaces<br />
|(Chen)<br />
|-<br />
|-<br />
|Oct. 25 <br />
|Emily Stark (Utah)<br />
| Action rigidity for free products of hyperbolic manifold groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 8<br />
|Max Forester (University of Oklahoma)<br />
|Spectral gaps for stable commutator length in some cubulated groups<br />
|(Dymarz)<br />
|-<br />
|Nov. 22<br />
|Yu Li (Stony Brook University)<br />
|On the structure of Ricci shrinkers<br />
|(Huang)<br />
|-<br />
|}<br />
<br />
==Fall Abstracts==<br />
<br />
===Ruobing Zhang===<br />
<br />
This talk centers on the degenerations of Calabi-Yau metrics. We will focus on the interactions between algebraic degenerations and metric convergence with highly singular behaviors in the collapsing case. As the complex structures degenerate, the collapsing Calabi-Yau metrics may exhibit various wild geometric properties with highly non-algebraic features.<br />
<br />
First, as motivating examples, we will describe our recent results on the new collapsing mechanisms of K3 surfaces. Next, we will switch to higher dimensions and we will exhibit some entirely new constructions of degenerating Calabi-Yau metrics which are expected to work in broader contexts. Complex structures degeneration will be accurately characterized by the bubbling and singularity analysis in a geometric manner.<br />
<br />
===Emily Stark===<br />
<br />
The relationship between the large-scale geometry of a group and its algebraic structure can be studied via three notions: a group's quasi-isometry class, a group's abstract commensurability class, and geometric actions on proper geodesic metric spaces. A common model geometry for groups G and G' is a proper geodesic metric space on which G and G' act geometrically. A group G is action rigid if every group G' that has a common model geometry with G is abstractly commensurable to G. For example, a closed hyperbolic n-manifold group is not action rigid for all n at least three. In contrast, we show that free products of closed hyperbolic manifold groups are action rigid. Consequently, we obtain the first examples of Gromov hyperbolic groups that are quasi-isometric but do not virtually have a common model geometry. This is joint work with Daniel Woodhouse.<br />
<br />
===Max Forester===<br />
<br />
I will discuss stable commutator length (scl) in groups, and some gap theorems for the scl spectrum. Such results say that for various groups, scl of an element is always either zero or is larger than some uniform constant. I will discuss the cases of right-angled Artin groups and certain right-angled Coxeter groups. This is joint work with Pallavi Dani, Ignat Soroko, and Jing Tao.<br />
<br />
===Yu Li===<br />
We develop a structure theory for non-collapsed Ricci shrinkers without any curvature condition. As an application, we show that any Ricci shrinker whose second eigenvalue of the curvature operator is positive must be a quotient of sphere.<br />
<br />
== Archive of past Geometry seminars ==<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 />
2010: [[Fall-2010-Geometry-Topology]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=18515Colloquia/Spring20202019-12-02T21:34:09Z<p>Gong: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 25 '''Monday 4-5 pm Room 911'''<br />
|Tatyana Shcherbina (Princeton)<br />
| [[# Tatyana Shcherbina (Princeton)| "Random matrix theory and supersymmetry techniques"]]<br />
|Roch<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao (University of Chicago)<br />
| [[#Tingran Gao (University of Chicago)| "Manifold Learning on Fibre Bundles"]]<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm Room 911'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Charlotte Chan<br />
|Flag varieties and representations of p-adic groups<br />
|Erman<br />
|-<br />
|Dec 9 '''Monday 4-5 pm'''<br />
|Hui Yu (Columbia)<br />
|[[#Hui Yu (Columbia)|Singular sets in obstacle problems]]<br />
|Tran<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|[[#Nick Higham (Manchester)|LAA lecture: Challenges in Multivalued Matrix Functions]]<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 29 '''Wednesday 4-5 pm'''<br />
|[https://ajzucker.wordpress.com/ Andy Zucker] (Lyon)<br />
|<br />
|Soskova/Lempp<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
<br />
Abstract: Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
<br />
Abstract: An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
<br />
=== Tatyana Shcherbina (Princeton) ===<br />
<br />
Title: Random matrix theory and supersymmetry techniques<br />
<br />
Abstract: Starting from the works of Erdos, Yau, Schlein with coauthors, the significant progress in understanding the universal behavior of many random graph and random matrix models were achieved. However for the random matrices with a special structure our understanding is still very limited. In this talk I am going to overview applications of another approach to the study of the local eigenvalues statistics in random matrix theory based on so-called supersymmetry techniques (SUSY). SUSY approach is based on the representation of the determinant as an integral over the Grassmann (anticommuting) variables. Combining this representation with the representation of an inverse determinant as an integral over the Gaussian complex field, SUSY allows to obtain an integral representation for the main spectral characteristics of random matrices such as limiting density, correlation functions, the resolvent's elements, etc. This method is widely (and successfully) used in the physics literature and is potentially very powerful but the rigorous control of the integral representations, which can be obtained by this method, is quite difficult, and it requires powerful analytic and statistical mechanics tools. In this talk we will discuss some recent progress in application of SUSY to the analysis of local spectral characteristics of the prominent ensemble of random band matrices, i.e. random matrices<br />
whose entries become negligible if their distance from the main diagonal exceeds a certain parameter called the band width. <br />
<br />
<br />
=== Tingran Gao (University of Chicago) ===<br />
<br />
Title: Manifold Learning on Fibre Bundles<br />
<br />
Abstract: Spectral geometry has played an important role in modern geometric data analysis, where the technique is widely known as Laplacian eigenmaps or diffusion maps. In this talk, we present a geometric framework that studies graph representations of complex datasets, where each edge of the graph is equipped with a non-scalar transformation or correspondence. This new framework models such a dataset as a fibre bundle with a connection, and interprets the collection of pairwise functional relations as defining a horizontal diffusion process on the bundle driven by its projection on the base. The eigenstates of this horizontal diffusion process encode the “consistency” among objects in the dataset, and provide a lens through which the geometry of the dataset can be revealed. We demonstrate an application of this geometric framework on evolutionary anthropology.<br />
<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
=== Charlotte Chan (MIT) ===<br />
<br />
Title: Flag varieties and representations of p-adic groups<br />
<br />
Abstract: In the 1950s, Borel, Weil, and Bott showed that the<br />
irreducible representations of a complex reductive group can be<br />
realized in the cohomology of line bundles on flag varieties. In the<br />
1970s, Deligne and Lusztig constructed a family of subvarieties of<br />
flag varieties whose cohomology realizes the irreducible<br />
representations of reductive groups over finite fields. I will survey<br />
these stories, explain recent progress towards finding geometric<br />
constructions of representations of p-adic groups, and discuss<br />
interactions with the Langlands program.<br />
<br />
=== Hui Yu (Columbia) ===<br />
<br />
Title: Singular sets in obstacle problems<br />
<br />
Abstract: One of the most important free boundary problems is the obstacle problem. The regularity of its free boundary has been studied for over half a century. In this talk, we review some classical results as well as exciting new developments. In particular, we discuss the recent resolution of the regularity of the singular set for the fully nonlinear obstacle problem. This talk is based on a joint work with Ovidiu Savin at Columbia University.<br />
<br />
<br />
=== Nick Higham (Manchester) ===<br />
<br />
Title: Challenges in Multivalued Matrix Functions<br />
<br />
Abstract: In this lecture I will discuss multivalued matrix functions that arise in solving various kinds of matrix equations. The matrix logarithm is the prototypical example, and my first interaction with Hans Schneider was about this function. Another example is the Lambert W function of a matrix, which is much less well known but has been attracting recent interest. A theme of the talk is the importance of choosing appropriate principal values and making sure that the correct choices of signs and branches are used,<br />
both in theory and in computation. I will give examples where incorrect results have previously been obtained.<br />
<br />
I focus on matrix inverse trigonometric and inverse hyperbolic functions, beginning by investigating existence and characterization. Turning to the principal values, various functional identities are derived, some of which are new even in the scalar case, including a “round trip” formula that relates acos(cos A) to A and similar formulas for the other inverse functions. Key tools used in the derivations are the matrix unwinding function and the matrix sign function.<br />
<br />
A new inverse scaling and squaring type algorithm employing a Schur decomposition and variable-degree Pade approximation is derived for computing acos, and it is shown how it can also be used to compute asin, acosh, and asinh.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<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]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=18449Colloquia/Spring20202019-11-18T17:05:04Z<p>Gong: /* Andrew Zimmer (LSU) */</p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao<br />
|<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results.<br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<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]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=18448Colloquia/Spring20202019-11-18T17:00:34Z<p>Gong: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao<br />
|<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
| Intrinsic and extrinsic geometries in several complex variables<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results. <br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<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]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Colloquia/Spring2020&diff=18446Colloquia/Spring20202019-11-18T16:59:04Z<p>Gong: </p>
<hr />
<div>= Mathematics Colloquium =<br />
<br />
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, '''unless otherwise indicated'''.<br />
<br />
<br />
<br />
==Fall 2019==<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 6 '''Room 911'''<br />
| Will Sawin (Columbia)<br />
| [[#Will Sawin (Columbia) | On Chowla's Conjecture over F_q[T] ]]<br />
| Marshall<br />
|-<br />
|Sept 13<br />
| [https://www.math.ksu.edu/~soibel/ Yan Soibelman] (Kansas State)<br />
|[[#Yan Soibelman (Kansas State)| Riemann-Hilbert correspondence and Fukaya categories ]]<br />
| Caldararu<br />
|<br />
|-<br />
|Sept 16 '''Monday Room 911'''<br />
| [http://mate.dm.uba.ar/~alidick/ Alicia Dickenstein] (Buenos Aires)<br />
|[[#Alicia Dickenstein (Buenos Aires)| Algebra and geometry in the study of enzymatic cascades ]]<br />
| Craciun<br />
|<br />
|-<br />
|Sept 20<br />
| [https://math.duke.edu/~jianfeng/ Jianfeng Lu] (Duke)<br />
|[[#Jianfeng Lu (Duke) | How to "localize" the computation?]]<br />
| Qin<br />
|<br />
|-<br />
|Sept 26 '''Thursday 3-4 pm Room 911'''<br />
| [http://eugeniacheng.com/ Eugenia Cheng] (School of the Art Institute of Chicago)<br />
| [[#Eugenia Cheng (School of the Art Institute of Chicago)| Character vs gender in mathematics and beyond ]]<br />
| Marshall / Friends of UW Madison Libraries<br />
|<br />
|-<br />
|Sept 27<br />
|<br />
|<br />
|-<br />
|Oct 4<br />
|<br />
|<br />
|-<br />
|Oct 11<br />
| Omer Mermelstein (Madison)<br />
| [[#Omer Mermelstein (Madison)| Generic flat pregeometries ]]<br />
|Andrews<br />
|<br />
|-<br />
|Oct 18<br />
| Shamgar Gurevich (Madison)<br />
| [[#Shamgar Gurevich (Madison) | Harmonic Analysis on GL(n) over Finite Fields ]]<br />
| Marshall<br />
|-<br />
|Oct 25<br />
|<br />
|-<br />
|Nov 1<br />
|Elchanan Mossel (MIT)<br />
|Distinguished Lecture<br />
|Roch<br />
|-<br />
|Nov 8<br />
|Jose Rodriguez (UW-Madison)<br />
|[[#Jose Rodriguez (UW-Madison) | Nearest Point Problems and Euclidean Distance Degrees]]<br />
|Erman<br />
|-<br />
|Nov 13 '''Wednesday 4-5pm'''<br />
|Ananth Shankar (MIT)<br />
|Exceptional splitting of abelian surfaces<br />
|-<br />
|Nov 20 '''Wednesday 4-5pm'''<br />
|Franca Hoffman (Caltech)<br />
|[[#Franca Hoffman (Caltech) | Gradient Flows: From PDE to Data Analysis]]<br />
|Smith<br />
|-<br />
|Nov 22<br />
| Jeffrey Danciger (UT Austin)<br />
| [[#Jeffrey Danciger (UT Austin) | "Affine geometry and the Auslander Conjecture"]]<br />
| Kent<br />
|-<br />
|Nov 29<br />
|Thanksgiving<br />
|<br />
|-<br />
|Dec 2 '''Monday 4-5pm'''<br />
|Tingran Gao<br />
|<br />
|Smith<br />
|-<br />
|Dec 4 '''Wednesday 4-5 pm'''<br />
|Andrew Zimmer<br />
|Gong<br />
|-<br />
|Dec 6<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Dec 11 '''Wednesday'''<br />
|Nick Higham (Manchester)<br />
|LAA lecture<br />
|Brualdi<br />
|<br />
|-<br />
|Dec 13<br />
|Reserved for job talk<br />
|<br />
|}<br />
<br />
==Spring 2020==<br />
<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|<br />
|-<br />
|Jan 24<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Jan 31<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 7<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 14<br />
|Reserved for job talk<br />
|<br />
|-<br />
|Feb 21<br />
|Shai Evra (IAS)<br />
|<br />
|Gurevich<br />
|<br />
|-<br />
|Feb 28<br />
|Brett Wick (Washington University, St. Louis)<br />
|<br />
|Seeger<br />
|-<br />
|March 6<br />
| Jessica Fintzen (Michigan)<br />
|<br />
|Marshall<br />
|-<br />
|March 13<br />
|<br />
|-<br />
|March 20<br />
|Spring break<br />
|<br />
|-<br />
|March 27<br />
|(Moduli Spaces Conference)<br />
|<br />
|Boggess, Sankar<br />
|-<br />
|April 3<br />
|Caroline Turnage-Butterbaugh (Carleton College)<br />
|<br />
|Marshall<br />
|-<br />
|April 10<br />
| Sarah Koch (Michigan)<br />
|<br />
| Bruce (WIMAW)<br />
|-<br />
|April 17<br />
|Song Sun (Berkeley)<br />
|<br />
|Huang<br />
|-<br />
|April 24<br />
|Natasa Sesum (Rutgers University)<br />
|<br />
|Angenent<br />
|-<br />
|May 1<br />
|Robert Lazarsfeld (Stony Brook)<br />
|Distinguished lecture<br />
|Erman<br />
|}<br />
<br />
== Abstracts ==<br />
<br />
<br />
===Will Sawin (Columbia)===<br />
<br />
Title: On Chowla's Conjecture over F_q[T]<br />
<br />
Abstract: The Mobius function in number theory is a sequences of 1s, <br />
-1s, and 0s, which is simple to define and closely related to the <br />
prime numbers. Its behavior seems highly random. Chowla's conjecture <br />
is one precise formalization of this randomness, and has seen recent <br />
work by Matomaki, Radziwill, Tao, and Teravainen making progress on <br />
it. In joint work with Mark Shusterman, we modify this conjecture by <br />
replacing the natural numbers parameterizing this sequence with <br />
polynomials over a finite field. Under mild conditions on the finite <br />
field, we are able to prove a strong form of this conjecture. The <br />
proof is based on taking a geometric perspective on the problem, and <br />
succeeds because we are able to simplify the geometry using a trick <br />
based on the strange properties of polynomial derivatives over finite <br />
fields.<br />
<br />
<br />
===Yan Soibelman (Kansas State)===<br />
<br />
Title: Riemann-Hilbert correspondence and Fukaya categories<br />
<br />
Abstract: In this talk I am going to discuss the role of Fukaya categories in the Riemann-Hilbert correspondence<br />
for differential, q-difference and elliptic difference equations in dimension one.<br />
This approach not only gives a unified answer for several versions of the Riemann-Hilbert correspondence but also leads to a natural formulation<br />
of the non-abelian Hodge theory in dimension one. It also explains why periodic monopoles<br />
should appear as harmonic objects in this generalized non-abelian Hodge theory.<br />
All that is a part of the bigger project ``Holomorphic Floer theory",<br />
joint with Maxim Kontsevich.<br />
<br />
<br />
===Alicia Dickenstein (Buenos Aires)===<br />
<br />
Title: Algebra and geometry in the study of enzymatic cascades<br />
<br />
Abstract: In recent years, techniques from computational and real algebraic geometry have been successfully used to address mathematical challenges in systems biology. The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need the determination of the parameters a priori, which can be theoretically or practically impossible.<br />
I will give a gentle introduction to general results based on the network structure. In particular, I will describe a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and include many networks that model post-translational modifications of proteins inside the cell. I will also outline recent methods to address the important question of multistationarity, in particular in the study of enzymatic cascades, and will point out some of the mathematical challenges that arise from this application.<br />
<br />
<br />
=== Jianfeng Lu (Duke) ===<br />
Title: How to ``localize" the computation?<br />
<br />
It is often desirable to restrict the numerical computation to a local region to achieve best balance between accuracy and affordability in scientific computing. It is important to avoid artifacts and guarantee predictable modelling while artificial boundary conditions have to be introduced to restrict the computation. In this talk, we will discuss some recent understanding on how to achieve such local computation in the context of topological edge states and elliptic random media.<br />
<br />
===Eugenia Cheng (School of the Art Institute of Chicago)===<br />
<br />
Title: Character vs gender in mathematics and beyond<br />
<br />
Abstract: This presentation will be based on my experience of being a female mathematician, and teaching mathematics at all levels from elementary school to grad school. The question of why women are under-represented in mathematics is complex and there are no simple answers, only many many contributing factors. I will focus on character traits, and argue that if we focus on this rather than gender we can have a more productive and less divisive conversation. To try and focus on characters rather than genders I will introduce gender-neutral character adjectives "ingressive" and "congressive" to replace masculine and feminine. I will share my experience of teaching congressive abstract mathematics to art students, in a congressive way, and the possible effects this could have for everyone in mathematics, not just women.<br />
<br />
===Omer Mermelstein (Madison)===<br />
<br />
Title: Generic flat pregeometries<br />
<br />
Abstract: In model theory, the tamest of structures are the strongly minimal ones -- those in which every equation in a single variable has either finitely many or cofinitely many solution. Algebraically closed fields and vector spaces are the canonical examples. Zilber’s conjecture, later refuted by Hrushovski, states that the source of geometric complexity in a strongly minimal structure must be algebraic. The property of "flatness" (strict gammoid) of a geometry (matroid) is that which guarantees Hrushovski's construction is devoid of any associative structure.<br />
The majority of the talk will explain what flatness is, how it should be thought of, and how closely it relates to hypergraphs and Hrushovski's construction method. Model theory makes an appearance only in the second part, where I will share results pertaining to the specific family of geometries arising from Hrushovski's methods.<br />
<br />
<br />
===Shamgar Gurevich (Madison)===<br />
<br />
Title: Harmonic Analysis on GL(n) over Finite Fields.<br />
<br />
Abstract: There are many formulas that express interesting properties of a finite group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the character ratio:<br />
<br />
trace(ρ(g)) / dim(ρ),<br />
<br />
for an irreducible representation ρ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of the mentioned type for analyzing certain random walks on G.<br />
<br />
Recently, we discovered that for classical groups G over finite fields there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant rank. <br />
<br />
This talk will discuss the notion of rank for the group GLn over finite fields, demonstrate how it controls the character ratio, and explain how one can apply the results to verify mixing time and rate for certain random walks.<br />
<br />
This is joint work with Roger Howe (Yale and Texas AM). The numerics for this work was carried by Steve Goldstein (Madison)<br />
<br />
<br />
===Jose Rodriguez (UW-Madison)===<br />
Determining the closest point to a model (subset of Euclidean space) is an important problem in many applications in science,<br />
engineering, and statistics. One way to solve this problem is by minimizing the squared Euclidean distance function using a gradient<br />
descent approach. However, when there are multiple local minima, there is no guarantee of convergence to the true global minimizer.<br />
An alternative method is to determine the critical points of an objective function on the model.<br />
In algebraic statistics, the models of interest are algebraic sets, i.e., solution sets to a system of multivariate polynomial equations. In this situation, the number of critical points of the squared Euclidean distance function on the model’s Zariski closure is a topological invariant called the Euclidean distance degree (ED degree).<br />
In this talk, I will present some models from computer vision and statistics that may be described as algebraic sets. Moreover,<br />
I will describe a topological method for determining a Euclidean distance degree and a numerical algebraic geometry approach for<br />
determining critical points of the squared Euclidean distance function.<br />
<br />
<br />
===Ananth Shankar (MIT)===<br />
An abelian surface 'splits' if it admits a non-trivial map to some elliptic curve. It is well known that the set of abelian surfaces that split are sparse in the set of all abelian surfaces. Nevertheless, we prove that there are infinitely many split abelian surfaces in arithmetic one-parameter families of generically non-split abelian surfaces. I will describe this work, and if time permits, mention generalizations of this result to the setting of K3 surfaces, as well as applications to the dynamics of hecke orbits. This is joint work with Tang, Maulik-Tang, and Shankar-Tang-Tayou.<br />
<br />
===Franca Hoffman (Caltech)===<br />
<br />
Title: Gradient Flows: From PDE to Data Analysis.<br />
<br />
Abstract: Certain diffusive PDEs can be viewed as infinite-dimensional gradient flows. This fact has led to the development of new tools in various areas of mathematics ranging from PDE theory to data science. In this talk, we focus on two different directions: model-driven approaches and data-driven approaches.<br />
In the first part of the talk we use gradient flows for analyzing non-linear and non-local aggregation-diffusion equations when the corresponding energy functionals are not necessarily convex. Moreover, the gradient flow structure enables us to make connections to well-known functional inequalities, revealing possible links between the optimizers of these inequalities and the equilibria of certain aggregation-diffusion PDEs.<br />
In the second part, we use and develop gradient flow theory to design novel tools for data analysis. We draw a connection between gradient flows and Ensemble Kalman methods for parameter estimation. We introduce the Ensemble Kalman Sampler - a derivative-free methodology for model calibration and uncertainty quantification in expensive black-box models. The interacting particle dynamics underlying our algorithm can be approximated by a novel gradient flow structure in a modified Wasserstein metric which reflects particle correlations. The geometry of this modified Wasserstein metric is of independent theoretical interest.<br />
<br />
=== Jeffrey Danciger (UT Austin) ===<br />
<br />
Title: Affine geometry and the Auslander Conjecture<br />
<br />
Abstract: The Auslander Conjecture is an analogue of Bieberbach’s theory of Euclidean crystallographic groups in the setting of affine geometry. It predicts that a complete affine manifold (a manifold equipped with a complete torsion-free flat affine connection) which is compact must have virtually solvable fundamental group. The conjecture is known up to dimension six, but is known to fail if the compactness assumption is removed, even in low dimensions. We discuss some history of this conjecture, give some basic examples, and then survey some recent advances in the study of non-compact complete affine manifolds with non-solvable fundamental group. <br />
Tools from the deformation theory of pseudo-Riemannian hyperbolic manifolds and also from higher Teichm&uuml;ller theory will enter the picture.<br />
<br />
=== Andrew Zimmer (LSU) ===<br />
<br />
Title: Intrinsic and extrinsic geometries in several complex variables<br />
<br />
Abstract: A bounded domain in complex Euclidean space, despite being one of the simplest types of manifolds, has a number of interesting geometric structures. When the domain is pseudoconvex, it has a natural intrinsic geometry: the complete Kaehler-Einstein metric constructed by Cheng-Yau and Mok-Yau. When the domain is smoothly bounded, there is also a natural extrinsic structure: the CR-geometry of the boundary. In this talk, I will describe connections between these intrinsic and extrinsic geometries. Then, I will discuss how these connections can lead to new analytic results. <br />
<br />
== Future Colloquia ==<br />
[[Colloquia/Fall 2020| Fall 2020]]<br />
<br />
== Past Colloquia ==<br />
<br />
[[Colloquia/Blank|Blank]]<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]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=18215Analysis Seminar2019-10-20T02:51:22Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#linktoabstract | Title ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Yifei Pan<br />
| Indiana University-Purdue University Fort Wayne<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Tamás Titkos<br />
| BBS University of Applied Sciences & Rényi Institute<br />
|[[#linktoabstract | Distance preserving maps on spaces of probability measures ]]<br />
| Street<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=18185Analysis Seminar2019-10-15T18:44:52Z<p>Gong: /* Abstracts */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#linktoabstract | Title ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=18184Analysis Seminar2019-10-15T04:48:57Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#linktoabstract | Title ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=18183Analysis Seminar2019-10-15T04:47:24Z<p>Gong: /* Abstracts */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact<br />
manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#linktoabstract | Title ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
===Laurent Stolovitch===<br />
<br />
<b>Linearization of neighborhoods of embeddings of complex compact manifolds </b><br />
<br />
In this work, we address the following question due to Grauert: if a neighborhood M of a holomorphically embedded complex compact manifold C is formally equivalent to another one, are two neighborhoods biholomorphically equivalent? We shall present the case where the other neighborhood is the neighborhood of the zero section of the normal bundle of C in M. The solution to this problem involves "small divisors problems". This is joint work with X. Gong.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=18182Analysis Seminar2019-10-15T04:31:30Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#Xiaocheng Li | An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$ ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#Jeff Galkowski | Concentration and Growth of Laplace Eigenfunctions ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#David Beltran | Regularity of the centered fractional maximal function ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Côte d'Azur<br />
|[[#Laurent Stolovitch | Linearization of neighborhoods of embeddings of complex compact<br />
manifolds ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|[[#Dominique Kemp | Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature]]<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#Kevin O'Neill | A Quantitative Stability Theorem for Convolution on the Heisenberg Group ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Joao Ramos<br />
| University of Bonn<br />
|[[#linktoabstract | Title ]]<br />
| Joris, Shaoming<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 7<br />
| Hong Wang<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Diogo Oliveira e Silva<br />
| University of Birmingham<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|-<br />
|May 5<br />
|Jonathan Hickman<br />
|University of Edinburgh<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
<br />
<br />
===Xiaocheng Li===<br />
<br />
Title: An Estimate for Spherical Functions on $\mathrm{SL}(3,\mathbb{R})$<br />
<br />
Abstract: We prove an estimate for spherical functions $\phi_\lambda(a)$ on $\mathrm{SL}(3,\mathbb{R})$, establishing uniform decay in the spectral parameter $\lambda$ when the group parameter $a$ is restricted to a compact subset of the abelian subgroup $\mathrm{A}$. In the case of $\mathrm{SL}(3,\mathbb{R})$, it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when the parameters $\lambda$ and $a$ vary.<br />
<br />
===Jeff Galkowski===<br />
<br />
<b>Concentration and Growth of Laplace Eigenfunctions</b><br />
<br />
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Finally, we use these ideas to understand a variety of measures of concentration; in each case obtaining quantitative improvements over the known bounds.<br />
<br />
===David Beltran===<br />
<br />
Title: Regularity of the centered fractional maximal function<br />
<br />
Abstract: I will report some recent progress regarding the boundedness of the map $f \mapsto |\nabla M_\beta f|$ from the endpoint space $W^{1,1}(\mathbb{R}^d)$ to $L^{d/(d-\beta)}(\mathbb{R}^d)$, where $M_\beta$ denotes the fractional version of the centered Hardy--Littlewood maximal function. A key step in our analysis is a relation between the centered and non-centered fractional maximal functions at the derivative level, which allows to exploit the known techniques in the non-centered case.<br />
<br />
This is joint work with José Madrid.<br />
<br />
===Dominique Kemp===<br />
<br />
<b>Decoupling for Real Analytic Surfaces Exhibiting Zero Curvature</b><br />
<br />
The celebrated l^2 decoupling theorem of Jean Bourgain and Ciprian Demeter presented a new perspective on a range of problems related to hypersurfaces with nonzero Gaussian curvature, such as exponential sum estimates, additive energy estimates, local smoothing, and counting solutions to Diophantine inequalities. The same authors also extended their theory to the n-dimensional cone. Following their steps, we prove optimal l^2 decoupling results for the remaining class of zero-curvature two-dimensional surfaces without umbilical points (the so-called tangent surfaces). We are also able to prove a decoupling theorem for the real analytic surfaces of revolution. These results should be viewed as partial progress toward the goal of proving a decoupling theorem for arbitrary real analytic hypersurfaces.<br />
<br />
<br />
===Kevin O'Neill===<br />
<br />
<b>A Quantitative Stability Theorem for Convolution on the Heisenberg Group </b><br />
<br />
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17911Analysis Seminar2019-09-17T15:37:08Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#José Madrid | On the regularity of maximal operators on Sobolev Spaces ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday, B139)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#Yakun Xi | Distance sets on Riemannian surfaces and microlocal decoupling inequalities ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#Joris Roos | L^p improving estimates for maximal spherical averages ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday, Room B139 VV)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|<b>Wednesday Oct 23 in B129</b><br />
|Dominique Kemp<br />
|Indiana University<br />
|tbd | tbd<br />
|Betsy<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===José Madrid===<br />
<br />
Title: On the regularity of maximal operators on Sobolev Spaces<br />
<br />
Abstract: In this talk, we will discuss the regularity properties (boundedness and<br />
continuity) of the classical and fractional maximal<br />
operators when these act on the Sobolev space W^{1,p}(\R^n). We will<br />
focus on the endpoint case p=1. We will talk about<br />
some recent results and current open problems.<br />
<br />
===Yakun Xi===<br />
<br />
Title: Distance sets on Riemannian surfaces and microlocal decoupling inequalities <br />
<br />
Abstract: In this talk, we discuss the generalization of the Falconer distance problem to the Riemannian setting. In particular, we extend the recent result of Guth-Iosevich-Ou-Wang for the distance set in the plane to general Riemannian surfaces. The key new ingredient is a family of refined decoupling inequalities associated with phase functions that satisfy Carleson-Sj\”olin condition. This is joint work with Iosevich and Liu.<br />
<br />
===Joris Roos===<br />
<br />
Title: L^p improving estimates for maximal spherical averages<br />
<br />
Abstract: For a given compact set of radii $E$ we will discuss $L^p$ improving properties of maximal spherical averages with a supremum over $E$.<br />
Our results are sharp up to endpoints for a large class of $E$. A new feature is that the optimal exponents depend on both, the upper Minkowski dimension and the Assouad dimension of the set $E$.<br />
Joint work with Tess Anderson, Kevin Hughes and Andreas Seeger.<br />
<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17731Analysis Seminar2019-09-02T16:29:27Z<p>Gong: /* Name */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Xiaojun Huang===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17730Analysis Seminar2019-09-02T16:28:38Z<p>Gong: </p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title: A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries<br />
<br />
Abstract: This is a joint work with Ming Xiao. We discuss how to construct a hyperbolic metric over a Stein space with spherical boundary. The technique we use is to employ holomorphic continuation along curves for multiple valued functions.<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17729Analysis Seminar2019-09-02T16:26:49Z<p>Gong: </p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 20 (2:25 PM Friday)<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17728Analysis Seminar2019-09-02T16:23:43Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| University of Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 20<br />
| Xiaojun Huang<br />
| Rutgers University–New Brunswick<br />
|[[#linktoabstract | A generalized Kerner theorem and hyperbolic metrics on Stein spaces with compact spherical boundaries ]]<br />
| Xianghong<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Xiaocheng Li<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Simon<br />
|-<br />
|Oct 8<br />
| Jeff Galkowski<br />
| Northeastern University<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Oct 15<br />
| David Beltran<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Bingyang Hu<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Francesco di Plinio<br />
| Washington University in St. Louis<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Street<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17566Analysis Seminar2019-07-19T12:42:19Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| Uni Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 15<br />
| Bassam Shayya<br />
| American University of Beirut <br />
|[[#linktoabstract | Title ]]<br />
| Andreas, Betsy<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| University of Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17565Analysis Seminar2019-07-19T12:41:07Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| Uni Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 15<br />
| Bassam Shayya<br />
| American University of Beirut <br />
|[[#linktoabstract | Title ]]<br />
| Andreas, Betsy<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| Université de Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17564Analysis Seminar2019-07-19T12:40:14Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| Uni Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 15<br />
| Bassam Shayya<br />
| American University of Beirut <br />
|[[#linktoabstract | Title ]]<br />
| Andreas, Betsy<br />
|-<br />
|Oct 22<br />
Laurent Stolovitch<br />
| IUniversité de Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17563Analysis Seminar2019-07-19T12:39:31Z<p>Gong: /* Analysis Seminar Schedule */</p>
<hr />
<div>'''Fall 2019 and Spring 2020 Analysis Seminar Series<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 10<br />
| José Madrid<br />
| UCLA<br />
|[[#linktoabstract | Title ]]<br />
| Andreas, David<br />
|-<br />
|Sept 13 (Friday)<br />
| Yakun Xi<br />
| Uni Rochester<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|Sept 17<br />
| Joris Roos<br />
| UW Madison<br />
|[[#linktoabstract | Title ]]<br />
| Brian<br />
|-<br />
|Sept 24<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 1<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 8<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Oct 15<br />
| Bassam Shayya<br />
| American University of Beirut <br />
|[[#linktoabstract | Title ]]<br />
| Andreas, Betsy<br />
|-<br />
|Oct 22<br />
| Laurent Stolovitch<br />
| IUniversité de Nice Sophia-Antipolis<br />
|[[#linktoabstract | Title ]]<br />
| Xianghong<br />
|-<br />
|Oct 29<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 5<br />
| Kevin O'Neill<br />
| UC Davis<br />
|[[#linktoabstract | Title ]]<br />
| Betsy<br />
|-<br />
|Nov 12<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 19<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Nov 26<br />
| No Seminar<br />
| <br />
|<br />
| <br />
|-<br />
|Dec 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Dec 10<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 21<br />
| No Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Jan 28<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 4<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 11<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 18<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Feb 25<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 3<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 10<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Mar 17<br />
| Spring Break!<br />
|<br />
|<br />
| <br />
|-<br />
|Mar 24<br />
| Oscar Dominguez<br />
| Universidad Complutense de Madrid<br />
|[[#linktoabstract | Title ]]<br />
| Andreas<br />
|-<br />
|Mar 31<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 7<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 14<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 21<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 28<br />
| No Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
<br />
===Name===<br />
<br />
Title<br />
<br />
Abstract<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17254Analysis Seminar2019-04-01T15:35:20Z<p>Gong: </p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
''Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
''The geometry of domains with negatively pinched Kaehler metrics''<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gonghttps://wiki.math.wisc.edu/index.php?title=Analysis_Seminar&diff=17253Analysis Seminar2019-04-01T15:34:08Z<p>Gong: </p>
<hr />
<div>'''Analysis Seminar<br />
'''<br />
<br />
The seminar will meet Tuesdays, 4:00 p.m. in VV B139, unless otherwise indicated.<br />
<br />
If you wish to invite a speaker please contact Brian at street(at)math<br />
<br />
===[[Previous Analysis seminars]]===<br />
<br />
= Analysis Seminar Schedule =<br />
{| cellpadding="8"<br />
!align="left" | date <br />
!align="left" | speaker<br />
|align="left" | '''institution'''<br />
!align="left" | title<br />
!align="left" | host(s)<br />
|-<br />
|Sept 11<br />
| Simon Marshall<br />
| UW Madison<br />
|[[#Simon Marshall | Integrals of eigenfunctions on hyperbolic manifolds ]]<br />
| <br />
|-<br />
|'''Wednesday, Sept 12'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|'''Friday, Sept 14'''<br />
| Gunther Uhlmann <br />
| University of Washington<br />
| Distinguished Lecture Series<br />
| See colloquium website for location<br />
|-<br />
|Sept 18<br />
| Grad Student Seminar<br />
| <br />
|<br />
|<br />
|-<br />
|Sept 25<br />
| Grad Student Seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Oct 9<br />
| Hong Wang<br />
| MIT<br />
|[[#Hong Wang | About Falconer distance problem in the plane ]]<br />
| Ruixiang <br />
|-<br />
|Oct 16<br />
| Polona Durcik<br />
| Caltech<br />
|[[#Polona Durcik | Singular Brascamp-Lieb inequalities and extended boxes in R^n ]]<br />
| Joris <br />
|-<br />
|Oct 23<br />
| Song-Ying Li<br />
| UC Irvine<br />
|[[#Song-Ying Li | Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold ]]<br />
| Xianghong <br />
|-<br />
|Oct 30<br />
|Grad student seminar<br />
|<br />
|<br />
|<br />
|-<br />
|Nov 6<br />
| Hanlong Fang<br />
| UW Madison<br />
|[[#Hanlong Fang | A generalization of the theorem of Weil and Kodaira on prescribing residues ]]<br />
| Brian<br />
|-<br />
||'''Monday, Nov. 12, B139'''<br />
| Kyle Hambrook<br />
| San Jose State University<br />
|[[#Kyle Hambrook | Fourier Decay and Fourier Restriction for Fractal Measures on Curves ]]<br />
| Andreas<br />
|-<br />
|Nov 13<br />
| Laurent Stolovitch<br />
| Université de Nice - Sophia Antipolis<br />
|[[#Laurent Stolovitch | Equivalence of Cauchy-Riemann manifolds and multisummability theory ]]<br />
|Xianghong<br />
|-<br />
|Nov 20<br />
| Grad Student Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Nov 27<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Dec 4<br />
| No Seminar<br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Jan 22<br />
| Brian Cook<br />
| Kent<br />
|[[#Brian Cook | Equidistribution results for integral points on affine homogenous algebraic varieties ]]<br />
| Street<br />
|-<br />
|Jan 29<br />
| No Seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
|<br />
|-<br />
|Feb 5, '''B239'''<br />
| Alexei Poltoratski<br />
| Texas A&M<br />
|[[#Alexei Poltoratski | Completeness of exponentials: Beurling-Malliavin and type problems ]]<br />
| Denisov<br />
|-<br />
|'''Friday, Feb 8'''<br />
| Aaron Naber<br />
| Northwestern University<br />
|[[#linktoabstract | A structure theory for spaces with lower Ricci curvature bounds ]]<br />
| See colloquium website for location<br />
|-<br />
|Feb 12<br />
| Shaoming Guo<br />
| UW Madison<br />
|[[#Shaoming Guo | Polynomial Roth theorems in Salem sets ]]<br />
| <br />
|-<br />
|'''Wed, Feb 13, B239'''<br />
| Dean Baskin<br />
| TAMU<br />
|[[# Dean Baskin | Radiation fields for wave equations ]]<br />
| Colloquium<br />
|-<br />
|'''Friday, Feb 15'''<br />
| Lillian Pierce<br />
| Duke<br />
|[[#Lillian Pierce | Short character sums ]]<br />
| Colloquium<br />
|-<br />
|'''Monday, Feb 18, 3:30 p.m, B239.'''<br />
| Daniel Tataru<br />
| UC Berkeley<br />
|[[#Daniel Tataru | A Morawetz inequality for water waves ]]<br />
| PDE Seminar<br />
|-<br />
|Feb 19<br />
| Wenjia Jing <br />
|Tsinghua University<br />
|Periodic homogenization of Dirichlet problems in perforated domains: a unified proof<br />
| PDE Seminar<br />
|-<br />
|Feb 26<br />
| No Seminar<br />
|<br />
|<br />
|-<br />
|Mar 5<br />
| Loredana Lanzani<br />
| Syracuse University<br />
|[[#Loredana Lanzani | On regularity and irregularity of the Cauchy-Szegő projection in several complex variables ]]<br />
| Xianghong<br />
|-<br />
|Mar 12<br />
| Trevor Leslie<br />
| UW Madison<br />
|[[#Trevor Leslie | Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time ]]<br />
|<br />
|-<br />
|Mar 19<br />
|Spring Break!<br />
| <br />
|<br />
|<br />
|-<br />
|Mar 26<br />
| No seminar<br />
| <br />
|[[#linktoabstract | ]]<br />
| <br />
|-<br />
|Apr 2<br />
| Stefan Steinerberger<br />
| Yale<br />
|[[#Stefan Steinerberger | Wasserstein Distance as a Tool in Analysis ]]<br />
| Shaoming, Andreas<br />
|-<br />
<br />
|Apr 9<br />
| Franc Forstnerič <br />
| Unversity of Ljubljana<br />
|[[#Franc Forstnerič | Minimal surfaces by way of complex analysis ]]<br />
| Xianghong, Andreas<br />
|-<br />
|Apr 16<br />
| Andrew Zimmer<br />
| Louisiana State University<br />
|[[#Andrew Zimmer | The geometry of domains with negatively pinched Kaehler metrics ]]<br />
| Xianghong<br />
|-<br />
|Apr 23<br />
| Person<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Sponsor<br />
|-<br />
|Apr 30<br />
| Reserved<br />
| Institution<br />
|[[#linktoabstract | Title ]]<br />
| Shaoming<br />
|-<br />
|}<br />
<br />
=Abstracts=<br />
===Simon Marshall===<br />
<br />
''Integrals of eigenfunctions on hyperbolic manifolds''<br />
<br />
Let X be a compact hyperbolic manifold, and let Y be a totally geodesic closed submanifold in X. I will discuss the problem of bounding the integral of a Laplace eigenfunction on X over Y, as the eigenvalue tends to infinity. I will present an upper bound for these integrals that is sharp on average, and briefly describe ongoing work with Farrell Brumley in which we attempt to produce eigenfunctions with very large periods.<br />
<br />
<br />
===Hong Wang===<br />
<br />
''About Falconer distance problem in the plane''<br />
<br />
If E is a compact set of Hausdorff dimension greater than 5/4 on the plane, we prove that there is a point x\in E such that the set of distances between x and E has positive Lebesgue measure. Our result improves upon Wolff's theorem for dim E> 4/3. This is joint work with Larry Guth, Alex Iosevich and Yumeng Ou. <br />
<br />
===Polona Durcik===<br />
<br />
''Singular Brascamp-Lieb inequalities and extended boxes in R^n''<br />
<br />
Brascamp-Lieb inequalities are L^p estimates for certain multilinear forms on functions on Euclidean spaces. In this talk we consider singular Brascamp-Lieb inequalities, which arise when one of the functions is replaced by a Calderon-Zygmund kernel. We focus on a family of multilinear forms in R^n with a certain cubical structure and discuss their connection to some patterns in positive density subsets in R^n. Based on joint works with V. Kovac and C. Thiele.<br />
<br />
<br />
===Song-Ying Li===<br />
<br />
''Estimates for the first positive eigenvalue of Kohn Laplacian on a pseudo-Hermitian manifold''<br />
<br />
In this talk, I will present my recent works with my collaborators on the lower bound and upper bounds estimates<br />
for the first positive eigenvalues of Kohn Laplacian and sub-Laplacian on a strictly pseudoconvex pseudo-Hermitian CR manifold,<br />
which include CR Lichnerowicz-Obata theorem for the lower and upper bounds for the first positive eigenvalue for the<br />
Kohn Laplacian on strictly pseudoconvex hypersurfaces.<br />
<br />
<br />
===Hanlong Fan===<br />
<br />
''A generalization of the theorem of Weil and Kodaira on prescribing residues''<br />
<br />
An old theorem of Weil and Kodaira says that: For a K\"ahler manifold X, there exists a closed meromorphic one-form with residue divisor D if and only if D is homologous to zero. In this talk, I will generalize Weil and Kodaira's criterion to non-K\"ahler manifolds.<br />
<br />
===Kyle Hambrook===<br />
<br />
''Fourier Decay and Fourier Restriction for Fractal Measures on Curves''<br />
<br />
I will discuss my recent work on some problems concerning<br />
Fourier decay and Fourier restriction for fractal measures on curves.<br />
<br />
===Laurent Stolovitch===<br />
<br />
''Equivalence of Cauchy-Riemann manifolds and multisummability theory''<br />
<br />
We apply the multisummability theory from Dynamical Systems to CR-geometry. As the main result, we show that two real-analytic hypersurfaces in $\mathbb C^2$ are formally equivalent, if and only if they are $C^\infty$ CR-equivalent at the respective point. As a corollary, we prove that all formal equivalences between real-algebraic Levi-nonflat hypersurfaces in $\mathbb C^2$ are algebraic (and in particular convergent). This is a joint work with I. Kossovskiy and B. Lamel.<br />
<br />
<br />
===Brian Cook===<br />
<br />
''Equidistribution results for integral points on affine homogenous algebraic varieties''<br />
<br />
Let Q be a homogenous integral polynomial of degree at least two. We consider certain results and questions concerning the distribution of the integral points on the level sets of Q.<br />
<br />
===Alexei Poltoratski===<br />
<br />
''Completeness of exponentials: Beurling-Malliavin and type problems''<br />
<br />
This talk is devoted to two old problems of harmonic analysis mentioned in the title. Both problems ask when a family of complex exponentials is complete (spans) an L^2-space. The Beruling-Malliavin problem was solved in the early 1960s and I will present its classical solution along with modern generalizations and applications. I will then discuss history and recent progress in the type problem, which stood open for more than 70 years.<br />
<br />
<br />
===Shaoming Guo===<br />
<br />
''Polynomial Roth theorems in Salem sets''<br />
<br />
Let P(t) be a polynomial of one real variable. I will report a result on searching for patterns of the form (x, x+t, x+P(t)) within Salem sets, whose Hausdorff dimension is sufficiently close to one. Joint work with Fraser and Pramanik. <br />
<br />
<br />
<br />
<br />
===Dean Baskin===<br />
<br />
''Radiation fields for wave equations''<br />
<br />
Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.<br />
<br />
===Lillian Pierce===<br />
<br />
''Short character sums''<br />
<br />
A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.<br />
<br />
===Loredana Lanzani===<br />
<br />
''On regularity and irregularity of the Cauchy-Szegő projection in several complex variables''<br />
<br />
This talk is a survey of my latest, and now final, collaboration with Eli Stein.<br />
<br />
It is known that for bounded domains $D$ in $\mathbb C^n$ that are of class $C^2$ and are strongly pseudo-convex, the Cauchy-Szegő projection is bounded in $L^p(\text{b}D, d\Sigma)$ for $1<p<\infty$. (Here $d\Sigma$ is induced Lebesgue measure.) We show, using appropriate worm domains, that this fails for any $p\neq 2$, when we assume that the domain in question is only weakly pseudo-convex. Our starting point are the ideas of Kiselman-Barrett introduced more than 30 years ago in the analysis of the Bergman projection. However the study of the Cauchy-Szegő projection raises a number of new issues and obstacles that need to be overcome. We will also compare these results to the analogous problem for the Cauchy-Leray integral, where however the relevant counter-example is of much simpler nature.<br />
<br />
===Trevor Leslie===<br />
<br />
''Energy Equality for the Navier-Stokes Equations at the First Possible Blowup Time''<br />
<br />
In this talk, we discuss the problem of energy equality for strong solutions of the Navier-Stokes Equations (NSE) at the first time where such solutions may lose regularity. Our approach is motivated by a famous theorem of Caffarelli, Kohn, and Nirenberg, which states that the set of singular points associated to a suitable weak solution of the NSE has parabolic Hausdorff dimension of at most 1. In particular, we furnish sufficient conditions for energy equality which depend on the dimension of the singularity set in addition to time and space integrability assumptions; in doing so we improve upon the classical results when attention is restricted to the first blowup time. When our method is inconclusive, we are able to quantify the possible failure of energy equality in terms of the lower local dimension and the ''concentration dimension'' of a certain measure associated to the solution. The work described is joint with Roman Shvydkoy (UIC).<br />
<br />
===Stefan Steinerberger===<br />
<br />
''Wasserstein Distance as a Tool in Analysis''<br />
<br />
Wasserstein Distance is a way of measuring the distance between two probability distributions (minimizing it is a main problem in Optimal Transport). We will give a gentle Introduction into what it means and then use it to prove (1) a completely elementary but possibly new and quite curious inequality for real-valued functions and (2) a statement along the following lines: linear combinations of eigenfunctions of elliptic operators corresponding to high frequencies oscillate a lot and vanish on a large set of co-dimension 1 (this is already interesting for trigonometric polynomials on the 2-torus, sums of finitely many sines and cosines, whose sum has to vanish on long lines) and (3) some statements in Basic Analytic Number Theory that drop out for free as a byproduct.<br />
<br />
===Franc Forstnerič===<br />
<br />
``Minimal surfaces by way of complex analysis''<br />
<br />
After a brief historical introduction, I will present some recent developments in the theory of minimal surfaces in Euclidean spaces which have been obtained by complex analytic methods. The emphasis will be on results pertaining to the global theory of minimal surfaces including Runge and Mergelyan approximation, the conformal Calabi-Yau problem, properly immersed and embedded minimal surfaces, and a new result on the Gauss map of minimal surfaces.<br />
<br />
===Andrew Zimmer===<br />
<br />
The geometry of domains with negatively pinched Kaehler metrics<br />
<br />
Every bounded pseudoconvex domain in C^n has a natural complete metric: the Kaehler-Einstein metric constructed by Cheng-Yau. When the boundary of the domain is strongly pseudoconvex, Cheng-Yau showed that the holomorphic sectional curvature of this metric is asymptotically a negative constant. In this talk I will describe some partial converses to this result, including the following: if a smoothly bounded convex domain has a complete Kaehler metric with close to constant negative holomorphic sectional curvature near the boundary, then the domain is strongly pseudoconvex. This is joint work with F. Bracci and H. Gaussier.<br />
<br />
<br />
<br />
=Extras=<br />
[[Blank Analysis Seminar Template]]</div>Gong