Colloquia: Difference between revisions

Revision as of 13:38, 22 September 2023

UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.

Fall 2023

date	speaker	title	host(s)
Sept 8	Tushar Das (University of Wisconsin-La Crosse)	Playing games on fractals: Dynamical & Diophantine	Stovall
Sept 15	John Schotland (Yale)	Nonlocal PDEs and Quantum Optics	Li
Sept 22	David Dumas(University of Illinois Chicago)	Geometry of surface group homomorphisms	Zimmer
Sept 29	no colloquium (see Monday)
Monday Oct 2 at 4 pm	Edriss Titi (Texas A&M University)	Distinguished lectures	Smith, Stechmann
Oct 13	Autumn Kent	The 0π Theorem
Oct 20	Sara Maloni (UVA)	TBA	Dymarz, Uyanik, GmMaW
Wednesday Oct 25 at 4 pm	Gigliola Staffilani (MIT)	The Schrödinger equations as inspiration of beautiful mathematics	Ifrim, Smith
Oct 27	Rodrigo Bañuelos (Purdue)	TBA	Stovall
Tuesday Oct 31 at 4 pm	Irit Dinur (The Weizmann Institute of Science)	Distinguished lectures	Gurevich
Wednesday Nov 1 at 4 pm	Irit Dinur (The Weizmann Institute of Science)	Distinguished lectures	Gurevich

Abstracts

Friday, September 8. Tushar Das

Playing games on fractals: Dynamical & Diophantine We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest, as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.

Friday, September 15. John Schotland

Nonlocal PDEs and Quantum Optics Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.

Friday, September 22. David Dumas

The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics. In this talk I will discuss and weave together two threads of research within this larger story: 1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view"). This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research.

Friday, October 13. Autumn Kent

A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.

Future Colloquia

Spring 2024

Past Colloquia

@@ Line 2: / Line 2: @@
-<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm. </b>
+<b>UW Madison mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.</b>
+==Fall 2023==
-<!--- in Van Vleck B239, '''unless otherwise indicated'''. --->
+{| cellpadding="8"
+!align="left" | date
+!align="left" | speaker
+!align="left" | title
+!align="left" | host(s)
+|
+|-
+|Sept 8
+|[https://www.uwlax.edu/profile/tdas/ Tushar Das] (University of Wisconsin-La Crosse)
+|Playing games on fractals: Dynamical & Diophantine |  Playing games on fractals: Dynamical & Diophantine
+|Stovall
+|-
+|Sept 15
+|[https://math.yale.edu/people/john-schotland John Schotland] (Yale)
+|Nonlocal PDEs and Quantum Optics
+|Li
+|-
+|Sept 22
+|[https://www.dumas.io/ David Dumas](University of Illinois Chicago)
+|Geometry of surface group homomorphisms
+|Zimmer
+|-
+|Sept 29
+|''no colloquium (see Monday)''
+|
+|
+|-
+|<b>Monday Oct 2 at 4 pm</b>
+|[https://www.math.tamu.edu/~titi/ Edriss Titi]  (Texas A&M University)
+|Distinguished lectures
+|Smith, Stechmann
+|-
+|Oct 13
+|Autumn Kent
+|The 0π Theorem
+|
+|-
+|Oct 20
+|Sara Maloni (UVA)
+|''TBA''
+|Dymarz, Uyanik, GmMaW
+|-
+|<b>Wednesday Oct 25 at 4 pm</b>
+|[https://math.mit.edu/~gigliola/ Gigliola Staffilani] (MIT)
+|The  Schrödinger equations as inspiration of beautiful mathematics
+|Ifrim, Smith
+|-
+|Oct 27
+|[https://www.math.purdue.edu/people/bio/banuelos/home Rodrigo Bañuelos] (Purdue)
+|''TBA''
+|Stovall
+|-
+|<b>Tuesday Oct 31 at 4 pm</b>
+|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)
+|Distinguished lectures
+|Gurevich
+|-
+|<b>Wednesday Nov 1 at 4 pm</b>
+|[https://www.wisdom.weizmann.ac.il/~dinuri/ Irit Dinur] (The Weizmann Institute of Science)
+|Distinguished lectures
+|Gurevich
+|}
+==Abstracts==
-== February 3, 2023, Friday at 4pm [https://sites.google.com/a/uwlax.edu/tdas/ Facundo Mémoli] (Ohio State University) ==
-(host: Lyu)
-The Gromov-Hausdorff distance between spheres.
-The Gromov-Hausdorff distance is a fundamental tool in Riemanian geometry (through the topology it generates) and is also utilized in applied geometry and topological data analysis as a metric for expressing the stability of methods which process geometric data (e.g. hierarchical clustering and persistent homology barcodes via the Vietoris-Rips filtration). In fact, distances such as the Gromov-Hausdorff distance or its Optimal Transport variants (i.e. the so-called Gromov-Wasserstein distances) are nowadays often invoked in applications related to data classification.
+'''Friday, September 8.  Tushar Das'''
-Whereas it is often easy to estimate the value of the Gromov-Hausdorff distance between two given metric spaces, its ''precise'' value is rarely easy to determine. Some of the best estimates follow from considerations related to both the stability of persistent homology and to Gromov's filling radius. However, these turn out to be non-sharp.
+Playing games on fractals: Dynamical & Diophantine
+We will present sketches of a program, developed in collaboration with Lior Fishman, David Simmons, and Mariusz Urbanski, which extends the parametric geometry of numbers (initiated by Wolfgang Schmidt and Leonhard Summerer) to Diophantine approximation for systems of m linear forms in n variables. Our variational principle (arXiv:1901.06602) provides a unified framework to compute Hausdorff and packing dimensions of a variety of sets of number-theoretic interest,  as well as their dynamical counterparts via the Dani correspondence. Highlights include the introduction of certain combinatorial objects that we call templates, which arise from a dynamical study of Minkowski’s successive minima in the geometry of numbers; as well as a new variant of Schmidt’s game designed to compute the Hausdorff and packing dimensions of any set in a doubling metric space. The talk will be accessible to students and faculty whose interests contain a convex combination of homogeneous dynamics, Diophantine approximation and fractal geometry.
-In this talk, I will describe these estimates and also results which permit calculating the precise value of the Gromov-Hausdorff between pairs of spheres (endowed with their usual geodesic distance). These results involve lower bounds which arise from a certain version of the Borsuk-Ulam theorem that is applicable to discontinuous maps, and also matching upper bounds which are induced from specialized constructions of (a posteriori optimal) ``correspondences" between spheres.
-== February 24, 2023, Cancelled/available ==
+'''Friday, September 15. John Schotland'''
-== March 3, 2023, Friday at 4pm [https://faculty.washington.edu/steinerb/ Stefan Steinerberger]  (University of Washington) ==
-Title: How curved is a combinatorial graph?
+Nonlocal PDEs and Quantum Optics
+Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.
-Abstract:   Curvature is one of the fundamental ingredients in differential geometry. People are increasingly interested in whether it is possible to think of combinatorial graphs as behaving like manifolds and a number of different notions of curvature have been proposed.  I will introduce some of the existing ideas and then propose a new notion based on a simple and explicit linear system of equations that is easy to compute. This notion satisfies a surprisingly large number of desirable properties -- connections to game theory (especially the von Neumann Minimax Theorem) and potential theory will be sketched; simultaneously, there is a certain "magic" element to all of this that is poorly understood and many open problems remain. I will also sketch some curious related problems that remain mostly open.  No prior knowledge of differential geometry (or graphs) is required.
-(hosts: Shaoming Guo, Andreas Seeger)
+'''Friday, September 22. David Dumas'''
-== March 8, 2023, Wednesday at 4pm [https://math.yale.edu/people/yair-minsky Yair Minsky]  (Yale University) ==
+The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical physics.  In this talk I will discuss and weave together two threads of research within this larger story:  1) the study of manifolds that are obtained by taking quotients of symmetric spaces (the "inside view") and 2) those obtained as quotients of domains in flag varieties (the "boundary view").  This discussion will start with classical objects--hyperbolic structures on surfaces---and continue into topics of ongoing research.
-'''''Distinguished lectures'''''
-Title:  Surfaces and foliations in hyperbolic 3-manifolds
+'''Friday, October 13. Autumn Kent'''
-Abstract: How does the geometric theory of hyperbolic 3-manifolds interact with the topological theory of foliations within them? Both points of view have seen profound developments over the past 40 years, and yet we have only an incomplete understanding of their overlap. I won't have much to add to this understanding! Instead, I will meander through aspects of both stories, saying a bit about what we know and pointing out some interesting questions.
+A celebrated theorem of Thurston tells us that among the many ways of filling in cusps of hyperbolic $3$--manfiolds, all but finitely many of them produce hyperbolic manifolds once again. This finiteness may be refined in a number of ways depending on the ``shape’’ of the cusp, and I’ll give a light and breezy discussion of joint work with K. Bromberg and Y. Minsky that allows shapes not covered by any of the previous theorems. This has applications such as answering questions asked in my 2010 job talk here at UW.
-(host: Kent)
+==Future Colloquia==
-== March 10, 2023, Friday at 4pm [https://math.yale.edu/people/yair-minsky Yair Minsky]  (Yale University) ==
-'''''Distinguished lectures'''''
-Title: End-periodic maps, via fibered 3-manifolds
-Abstract: In the second lecture I will focus on some joint work with Michael Landry and Sam Taylor. Thurston showed how a certain ``spinning<nowiki>''</nowiki> construction in a fibered 3-manifold produces a depth-1 foliation, which is described by an end-periodic map of an infinite genus surface. The dynamical properties of such maps were then studied by Handel-Miller, Cantwell-Conlon-Fenley and others. We show how to reverse this construction, obtaining every end-periodic map from spinning in a fibered manifold. This allows us to recover the dynamical features of the map, and more, directly from the more classical theory of fibered manifolds.
-(host: Kent)
-== March 24, 2023 , Friday at 4pm  [https://www.carolynrabbott.com/ Carolyn Abbott] (Brandeis University) ==
-'''Title''': Boundaries, boundaries, and more boundaries
-'''Abstract:''' It is possible to learn a lot about a group by studying how it acts on various metric spaces. One particularly interesting (and ubiquitous) class of groups are those that act nicely on negatively curved spaces, called hyperbolic groups. Since their introduction by Gromov in the 1980s, hyperbolic groups and their generalizations have played a central role in geometric group theory. One fruitful tool for studying such groups is their boundary at infinity. In this talk, I will discuss two generalizations of hyperbolic groups, relatively hyperbolic groups and hierarchically hyperbolic groups, and describe boundaries of each. I will describe various relationships between these boundaries and explain how the hierarchically hyperbolic boundary characterizes relative hyperbolicity among hierarchically hyperbolic groups.  This is joint work with Jason Behrstock and Jacob Russell.
-== March 31, 2023 , Friday at 4pm [http://www.math.toronto.edu/balint/ Bálint Virág] (University of Toronto) ==
-'''Title:''' Random plane geometry -- a gentle introduction
-'''Abstract:''' Consider Z^2, and assign a random length of 1 or 2 to each edge based on independent fair coin tosses. The resulting random geometry, first passage percolation, is conjectured to have a scaling limit. Most random plane geometric models (including hidden geometries) should have the same scaling limit. I will explain the basics of the limiting geometry, the "directed landscape", and its relation to traffic jams, tetris, coffee stains and random matrices.
-(host: Valko)
-== April 7, 2023, Friday at 4pm  [https://www.mi.fu-berlin.de/math/groups/fluid-dyn/members/rupert_klein.html Rupert Klein] (FU Berlin) ==
-'''''Wasow lecture'''''
-Title: Mathematics: A key to climate research
-Abstract: Mathematics in climate research is often thought to be mainly a provider of techniques for solving, e.g., the atmosphere and ocean flow equations. Three examples elucidate that its role is much broader and deeper:
-) Climate modelers often employ reduced forms of “the flow equations” for efficiency. Mathematical analysis helps assessing the regimes of validity of such models and defining conditions under which they can be solved robustly.
-) Climate is defined as “weather statistics”, and climate research investigates its change in time in our “single realization of Earth” with all its complexity. The required reliable notions of time dependent statistics for sparse data in high dimensions, however, remain to be established. Recent mathematical research offers advanced data analysis techniques that could be “game changing” in this respect.
-) Climate research, economy, and the social sciences are to generate a scientific basis for informed political decision making. Subtle misunderstandings often hamper systematic progress in this area. Mathematical formalization can help structuring discussions and bridging language barriers in interdisciplinary research.
-(hosts: Smith, Stechmann)
-== April 21, 2023, Friday at 4pm [https://sternber.pages.iu.edu/ Peter Sternberg]  (Indiana University) ==
-(hosts: Feldman, Tran)
-Title: A family of toy problems modeling liquid crystals exhibiting large disparity in the elastic coefficients.
-Abstract: Certain classes of liquid crystals have been found to strongly favor particular types of deformations over others; for example, the cost of splay may greatly exceed the cost of bend or twist. In a series of studies with Dmitry Golovaty (Akron), Michael Novack (UT Austin) and Raghav Venkatraman (Courant), we explore the implications of assuming various asymptotic regimes for the elastic constants. Through a mixture of formal and rigorous analysis, along with computations, we identify the limiting behavior of minimizers to the associated energies. We find that a variety of singular structures emerge corresponding to jumps in the profile of these limiting minimizers that effectively save on the cost of splay, bend or twist—whichever is assumed to be most expensive.
-== April 28, 2023, Friday at 4pm [https://nqle.pages.iu.edu/ Nam Q. Le]  (Indiana University) ==
-Title: Hessian eigenvalues and hyperbolic polynomials
-Abstract: Hessian eigenvalues are natural nonlinear analogues of the classical Dirichlet eigenvalues. The Hessian eigenvalues and their corresponding eigenfunctions are expected to share many analytic and geometric properties (such as uniqueness, stability, max-min principle, global smoothness, Brunn-Minkowski inequality, convergence of numerical schemes, etc) as their Dirichlet counterparts. In this talk, I will discuss these issues and some recent progresses in various geometric settings. I will also explain the unexpected role of hyperbolic polynomials in our analysis. I will not assume any familiarity with these concepts.
-== May 5, 2023, Friday at 4pm [https://www.math.ucdavis.edu/~gravner/ Janko Gravner]  (UC Davis) ==
-Title: Long-range nucleation
-Abstract: Nucleation is a mechanism by which one equilibrium displaces another through formation of small unstoppable nuclei. Typically, nucleation is local, as the size of the nuclei is much smaller than the time scale of convergence to the new state. We will discuss a few simple models where nuclei are not small in diameter but instead are a result of lower-dimensional structures that grow and interact significantly before most of the space is affected. Analysis of such models includes a variety of combinatorial and probabilistic methods.
-== Future Colloquia ==
-[[Colloquia/Fall2023|Fall 2023]]
 [[Colloquia/Spring2024|Spring 2024]]
 == Past Colloquia ==
+[[Colloquia/Spring2023|Spring 2023]]
 [[Colloquia/Fall2022|Fall 2022]]