Colloquia: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
VisualWikitext
(Undo revision 20759 by Jose (talk))
(366 intermediate revisions by 30 users not shown)
Line 2: Line 2:




<b>UW Madison mathematics Colloquium is ONLINE 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
|}


=Spring 2021=
==Abstracts==


== January 27, 2021 '''[Wed 4-5pm]''', [https://sites.google.com/view/morganeaustern/home Morgane Austern] (Microsoft Research) ==


(Hosted by Roch)


'''Asymptotics of learning on dependent and structured random objects'''
'''Friday, September 8.  Tushar Das'''


Classical statistical inference relies on numerous tools from probability theory to study
Playing games on fractals: Dynamical & Diophantine
the properties of estimators. However, these same tools are often inadequate to study
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.
modern machine problems that frequently involve structured data (e.g networks) or
complicated dependence structures (e.g dependent random matrices). In this talk, we
extend universal limit theorems beyond the classical setting.


Firstly, we consider distributionally “structured” and dependent random object–i.e
random objects whose distribution are invariant under the action of an amenable group.
We show, under mild moment and mixing conditions, a series of universal second and
third order limit theorems: central-limit theorems, concentration inequalities, Wigner
semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by
a series of examples in machine learning, network and information theory. Secondly
by building on these results, we establish the asymptotic distribution of the cross-
validated risk with the number of folds allowed to grow at an arbitrary rate. Using
this, we study the statistical speed-up of cross validation compared to a train-test split
procedure, which reveals surprising results even when used on simple estimators.


== January 29, 2021, [https://sites.google.com/site/isaacpurduemath/ Isaac Harris] (Purdue) ==
'''Friday, September 15. John Schotland'''


(Hosted by Smith)
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.


'''Direct Sampling Algorithms for Inverse Scattering'''


In this talk, we will discuss a recent qualitative imaging method referred to as the Direct Sampling Method for inverse scattering. This method allows one to recover a scattering object by evaluating an imaging functional that is the inner-product of the far-field data and a known function. It can be shown that the imaging functional is strictly positive in the scatterer and decays as the sampling point moves away from the scatterer. The analysis uses the factorization of the far-field operator and the Funke-Hecke formula. This method can also be shown to be stable with respect to perturbations in the scattering data. We will discuss the inverse scattering problem for both acoustic and electromagnetic waves. This is joint work with A. Kleefeld and D.-L. Nguyen.
'''Friday, September 22. David Dumas'''


== February 1, 2021 '''[Mon 4-5pm]''', [https://services.math.duke.edu/~nwu/index.htm Nan Wu] (Duke) ==
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.


(Hosted by Roch)


'''From Manifold Learning to Gaussian Process Regression on Manifolds'''
'''Friday, October 13. Autumn Kent'''


In this talk, I will review the concepts in manifold learning and discuss a famous manifold learning algorithm, the Diffusion Map. I will talk about my recent research results which theoretically justify that the Diffusion Map reveals the underlying topological structure of the dataset sampled from a manifold in a high dimensional space. Moreover, I will show the application of these theoretical results in solving the regression problems on manifolds and ecological problems in real life.
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.


== February 5, 2021, [https://hanbaeklyu.com/ Hanbaek Lyu] (UCLA) ==
==Future Colloquia==


(Hosted by Roch)
[[Colloquia/Spring2024|Spring 2024]]


'''Dictionary Learning from dependent data samples and networks'''
== Past Colloquia ==
 
Analyzing group behavior of systems of interacting variables is a ubiquitous problem in many fields including probability, combinatorics, and dynamical systems. This problem also naturally arises when one tries to learn essential features (dictionary atoms) from large and structured data such as networks. For instance, independently sampling some number of nodes in a sparse network hardly detects any edges between adjacent nodes. Instead, we may perform a random walk on the space of connected subgraphs, which will produce more meaningful but correlated samples. As classical results in probability were first developed for independent variables and then gradually generalized for dependent variables, many algorithms in machine learning first developed for independent data samples now need to be extended to correlated data samples. In this talk, we discuss some new results that accomplish this including some for online nonnegative matrix and tensor factorization for Markovian data. A unifying technique for handling dependence in data samples we develop is to condition on the distant past, rather than the recent history. As an application, we present a new approach for learning "basis subgraphs" from network data, that can be used for network denoising and edge inference tasks. We illustrate our method using several synthetic network models as well as Facebook, arXiv, and protein-protein interaction networks, that achieve state-of-the-art performance for such network tasks when compared to several recent methods.
 
== February 8, 2021 '''[Mon 4-5pm]''', [https://sites.google.com/view/mndaoud/home Mohamed Ndaoud] (USC) ==
 
(Hosted by Roch)
 
'''SCALED MINIMAX OPTIMALITY IN HIGH-DIMENSIONAL LINEAR REGRESSION: A NON-CONVEX ALGORITHMIC REGULARIZATION APPROACH'''
 
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies strongly on the knowledge of the true sparsity parameter s. In this paper, we present a novel fast procedure for estimation in the high dimensional linear regression. Taking advantage of the interplay between estimation, support recovery and optimization we achieve both optimal statistical accuracy and fast convergence. The main advantage of our procedure is that it is fully adaptive, making it more practical than state of the art IHT methods. Our procedure achieves optimal statistical accuracy faster than, for instance, classical algorithms for the Lasso. Moreover, we establish sharp optimal results for both estimation and support recovery. As a consequence, we present a new iterative hard thresholding algorithm for high dimensional linear regression that is scaled minimax optimal (achieves the estimation error of the oracle that knows the sparsity pattern if possible), fast and adaptive.
 
== February 12, 2021, [https://sites.math.washington.edu/~blwilson/ Bobby Wilson] (University of Washington) ==
 
(Hosted by Smith)
 
== February 17, 2021 '''[Wed 9-10am]''', [https://www.math.ias.edu/~visu/ Visu Makam] (IAS)==
 
(Hosted by Roch)
 
'''Algorithms in invariant theory, connections and applications'''
 
For over a century, computation has played a key role in the development of invariant theory, a subject that studies symmetries captured by group actions. Over the years, major computational advances such as the advent of the digital computer, the discovery of Grobner basis techniques, the development of rigorous notions of computational complexity, etc have served as a stimulus for invariant theory. The perspective adopted in this talk will be contrary — I will explain how developments in invariant theory can inform and make progress on fundamental problems in computational subjects such as complexity theory and statistics.
 
I will discuss how central problems in complexity such as the celebrated P vs NP problem, graph isomorphism, and identity testing arise in the context of invariant theory, focusing on recent results in invariant theory that shed new light on identity testing. I will also outline the challenges going forward in this exciting and rapidly developing field. With regard to statistics, a surprising connection was discovered last year between stability notions in invariant theory and maximum likelihood estimation for a special class of statistical models. This connection allows for invariant theoretic approaches to statistical questions, e.g., we can give exact sample size thresholds for the widely used matrix (and tensor) normal models by utilizing results on quiver representations, castling transforms, etc. I will also briefly point at some exciting current and future directions in this context. No special background will be assumed in this talk.
 
== February 19, 2021, [http://www.mauricefabien.com/ Maurice Fabien] (Brown)==
 
(Hosted by Smith)
 
'''A hybridizable discontinuous method for flow and transport phenomena in porous media'''
 
We present an efficient computational method for the approximation of solutions to partial differential equations that model flow and transport phenomena in porous media. These problems can be challenging to solve as the governing equations are coupled, nonlinear, and material properties are often highly varying and discontinuous. The high-order implicit hybridizable discontinuous method (HDG) is utilized for the discretization, which significantly reduces the computational cost. The HDG method is high-order accurate, locally mass-conservative, allows us to use unstructured complicated meshes, and enables the use of static condensation. We demonstrate that the HDG method is able to efficiently generate high-fidelity simulations of flow and transport phenomena in porous media. Several challenging benchmarks are used to verify and validate the method in heterogeneous porous media.
 
== February 26, 2021, [https://www.math.ias.edu/avi/home Avi Wigderson] (Princeton IAS) ==
 
(Hosted by Gurevich)
 
== March 12, 2021, [https://gauss.math.yale.edu/~il282/ Ivan Losev] (Yale) ==
 
(Hosted by Gurevich)
 
'''Modular representations of semisimple Lie algebras'''


Representation theory seeks to understand ways in which a
[[Colloquia/Spring2023|Spring 2023]]
given algebraic object (a group, an associative algebra, a Lie algebra
etc.) can be represented via linear operators on a vector space over a field.
What the representations are going to look like very much depends on the field
in question, and, in particular, on its characteristic.
Most important questions are settled in characteristic 0, for example,
when we work over the complex numbers. But in the case of postive
characteristic fields, which the word ``modular'' refers to, even basic
questions are wide open.   


In my talk I will concentrate on one of the most important algebraic
[[Colloquia/Fall2022|Fall 2022]]
objects, semisimple Lie algebras, and explain what we know about
about their irreducible (=no subrepresentations) modular representations.
I will start with the case of sl_2 explaining the results of Rudakov
and Shafarevich from 1967 describing the irreducible representations.
Then I will talk about recent work on the general case including my
paper with Bezrukavnikov from 2020, where we get the most explicit
description of irreducible representations available to date. Our primary
tool is relating the modular representations of semisimple Lie algebras
to the (affine) Hecke category, the most fundamental object of modern
Representation theory.


== March 26, 2021, [] ==
[[Spring 2022 Colloquiums|Spring 2022]]


(Hosted by )
[[Colloquia/Fall2021|Fall 2021]]


== April 9, 2021 '''[8pm]''', [https://web.math.princeton.edu/~weinan/ Weinan E] (Princeton) ==
[[Colloquia/Spring2021|Spring 2021]]
 
'''Hans Schneider LAA Lecture''' (Hosted by Shen)
 
== April 23, 2021, [] ==
 
(Hosted by )
 
 
 
 
== Past Colloquia ==


[[Colloquia/Fall2020|Fall 2020]]
[[Colloquia/Fall2020|Fall 2020]]

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

Spring 2023

Fall 2022

Spring 2022

Fall 2021

Spring 2021

Fall 2020

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012

WIMAW

Retrieved from "https://wiki.math.wisc.edu/index.php?title=Colloquia&oldid=25295"