Colloquia: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
VisualWikitext
No edit summary
No edit summary
 
(250 intermediate revisions by 27 users not shown)
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 unless otherwise noted. </b>


<!--- in Van Vleck B239, '''unless otherwise indicated'''. --->
<!--- in Van Vleck B239, '''unless otherwise indicated'''. --->


=Fall 2021=


== September 17, 2021, Social Sciences 5208 + [http://128.104.155.144/ClassroomStreams/socsci5208_stream.html Live Stream], [https://markshus.wixsite.com/math Mark Shusterman] (Harvard) ==
==Fall 2023==


(hosted by Gurevich)
{| 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
|
|
|
|-
|<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)
|
|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)
|
|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
|}


'''Finitely Presented Groups in Arithmetic Geometry'''
==Abstracts==


I will report on recent works, in part joint with Esnault—Srinivas, and with Jarden, on the finite presentability of several (profinite) groups arising in algebraic geometry and in number theory. These results build on a cohomological criterion of Lubotzky involving Euler characteristics. I will try to explain the analogy, rooted in arithmetic topology, between these results and classical facts about fundamental groups of three-dimensional manifolds.


== September 24, 2021, B239 + [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom stream], [https://math.wisc.edu/staff/paul-sean/ Sean Paul] (UW-Madison) ==
'''The Tian-Yau-Donaldson conjecture for general polarized manifolds'''


According to the Yau-Tian-Donaldson conjecture, the existence of a constant scalar curvature Kähler (cscK) metric in the cohomology class of an ample line bundle L on a compact complex manifold X should be equivalent to an algebro-geometric "stability condition" satisfied by the pair (X,L).  The cscK metrics are the critical points of Mabuchi's K-energy functional M, defined on the space of Kähler potentials, and an important result of Chen-Cheng shows that cscK metrics exist iff M satisfies a standard growth condition (coercivity/properness). Recently the speaker has shown that the K-energy is indeed proper if and only if the polarized manifold is stable. The stability condition is closely related to the classical notion of Hilbert-Mumford stability.  The speaker will give a non-technical general account of the many areas of mathematics that are involved in the proof. In particular, he hopes to discuss the surprising role played by arithmetic geometry​in the spirit of Arakelov, Faltings, and Bismut-Gillet- Soule.
'''Friday, September 8.  Tushar Das'''


== October 1, 2021, B239 + [http://go.wisc.edu/wuas48 Live stream], [https://people.math.wisc.edu/~andreic/ Andrei Caldararu] (UW-Madison) ==
Playing games on fractals: Dynamical & Diophantine
'''Yet another Moonshine'''
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.


The j-function, introduced by Felix Klein in 1879, is an essential ingredient in the study of elliptic curves. It is Z-periodic on the complex upper half-plane, so it admits a Fourier expansion. The original Monstrous Moonshine conjecture, due to McKay and Conway/Norton in the 1980s, relates the Fourier coefficients of the j-function around the cusp to dimensions of irreducible representations of the Monster simple group. It was proved by Borcherds in 1992.


In my talk I will try to give a rudimentary introduction to modular forms, explain Monstrous Moonshine, and discuss a new version of it obtained in joint work with Yunfan He and Shengyuan Huang.  Our version involves studying the j-function around CM points (so-called Landau-Ginzburg points in the physics literature) and expanding with respect to a coordinate which arises naturally in string theory.
'''Friday, September 15. John Schotland'''


== October 8, 2021, [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom] + live video on the 9th floor, [https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (University of Oxford) ==
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.


('''Wasow lecture'''; hosted by Thiffeault)
'''Friday, September 22. David Dumas'''


'''Asymptotics beyond all orders: the devil's invention?'''
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.


"Divergent series are the invention of the devil, and it is shameful to base on them any demonstration whatsoever." --- N. H. Abel.
'''Friday, October 13. Autumn Kent'''


The lecture will introduce the concept of an asymptotic series, showing how useful divergent series can be, despite Abel's reservations. We will then discuss Stokes' phenomenon, whereby the coefficients in the series appear to change discontinuously. We will show how understanding Stokes' phenomenon is the key which allows us to determine the qualitative and quantitative behaviour of the solution in many practical problems. Examples will be drawn from the areas of surface waves on fluids, crystal growth, dislocation dynamics, and Hele-Shaw flow.
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.


== October 11, 13, 15, 2021, [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom],  '''[Mon, Wed, Fri 4-5pm]''', [https://www.maths.usyd.edu.au/u/geordie/ Geordie Williamson] (University of Sydney) ==
==Future Colloquia==


('''Distinguished Lecture Series'''; hosted by Gurevich)
[[Colloquia/Spring2024|Spring 2024]]


'''Geometric representation theory and modular representations'''
== Past Colloquia ==
 
Representation theory is the study of linear symmetry. We are interested in all ways in which a group can arise as the symmetries of a vector space. Representation theory is a remarkably rich subject, with deep connections to number theory, combinatorics, algebraic geometry, differential geometry, theoretical physics and beyond. This lecture series will focus on modular representations, i.e. those representations where our vector spaces are over a field of characteristic p. I will try to highlight some of the main questions in the field and why we are interested in answering them. It is remarkable how much is still unknown and how hard some of these questions are. I will explain the role played by geometric representation theory in our attempts to understand these questions. A fascinating blend of algebra, algebraic geometry, category theory and algebraic topology is informing our understanding of basic questions. Much remains to be understood!
 
== October 22, 2021, [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom],  [https://math.berkeley.edu/people/faculty/vera-serganova Vera Serganova] (UC Berkeley) ==
 
(hosted by Gurevich/Gorin)
 
'''Supersymmetry and tensor categories'''
 
I will explain how representation theory of supergroups and
supergeometry are related to general theory of tensor categories,
present old and new results and open questions
in the field. We will see how universal tensor categories can be
constructed using supergroups and discuss analogy between super
representation theory and representation theory over the fields of
positive characteristic.
 
== October 29, 2021, [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom], [https://web.math.princeton.edu/~aionescu/ Alexandru Ionescu] (Princeton University) ==
 
(hosted by Wainger)
 
'''Polynomial averages and pointwise ergodic theorems on nilpotent groups'''
 
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.
 
== November 5, 2021,  B239 + [http://go.wisc.edu/wuas48 Live stream], [https://faculty.washington.edu/jathreya/ Jayadev S. Athreya] (University of Washington) ==
 
(hosted by Uyanik)
 
'''Surfaces and Point Processes'''
 
We'll give several concrete examples of how to go from the geometry of surfaces to the study of point processes, following work of Siegel, Veech, Masur, Eskin, Mirzakhani, Wright, and others. We'll discuss how this "probabilistic" perspective helps inform both the direction of questions one asks, as well as providing ideas of how to prove things. We'll discuss some pieces of joint work with Cheung-Masur, Margulis, and Arana-Herrera.
 
== November 12, 2021, [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 Zoom], [https://sites.tufts.edu/kasso/ Kasso Okoudjou] (Tufts University) ==


(hosted by Stovall)
[[Colloquia/Spring2023|Spring 2023]]


'''An exploration in analysis on fractals '''
[[Colloquia/Fall2022|Fall 2022]]


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.
[[Spring 2022 Colloquiums|Spring 2022]]


== November 19, 2021 , B239 + [http://go.wisc.edu/wuas48 Live stream],  [https://math.wisc.edu/staff/ai-albert/  Albert Ai](UW-Madison) ==
[[Colloquia/Fall2021|Fall 2021]]
 
(reserved by the hiring committee)
 
''' Low regularity solution for quasilinear PDEs'''
 
In this talk, we will consider the low regularity well-posedness problem for a pair of quasilinear dispersive PDEs: the nonlinear wave equation, and the water waves equations. Two classical methods, energy estimates and Strichartz estimates, have historically yielded substantial but partial results toward advancing the low regularity theory. We will see how, using a special structure of the equations known as a normal form structure, combined with tools from harmonic and microlocal analysis, we can refine these classical methods to drastically improve the known results for low regularity well-posedness.
 
== December 1, 2021, Wednesday at 4pm in B239 + [http://go.wisc.edu/wuas48 Live stream], [https://www.math.ucla.edu/~brianrl/ Brian Lawrence] (UCLA) ==
 
(reserved by the hiring committee)
 
== December 3, 2021, Friday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 ZOOM] + live video in B239, [https://people.wgtn.ac.nz/martino.lupini Martino Lupini] (Victoria University of Wellington) ==
 
(reserved by the hiring committee)
 
'''Borel-definable Algebraic Topology'''
 
In this talk, I will explain how ideas and methods from logic can be used to obtain refinements of classical invariants from homological algebra and algebraic topology. I will then present some applications to classification problems in topology. This is joint work with Jeffrey Bergfalk and Aristotelis Panagiotopoulos.
 
== December 6, 2021, Monday at 4pm on [https://uwmadison.zoom.us/j/93283927523?pwd=S3V6Nlh4bUhYc0F5QzNabi9RMSthUT09 ZOOM], [https://sites.google.com/site/michaellipnowski/ Michael Lipnowski]  (McGill) ==
 
(reserved by the hiring committee)
 
== December 8, 2021, Wednesday at 4pm in B239  + [http://go.wisc.edu/wuas48 Live stream], [https://padmask.github.io/ Padmavathi Srinivasan] (University of Georgia) ==
 
(reserved by the hiring committee)
 
== December 10, 2021, Friday at 4pm in B239  + [http://go.wisc.edu/wuas48 Live stream], [http://www-personal.umich.edu/~apisa/ Paul Apisa] (University of Michigan) ==
 
(reserved by the hiring committee)
 
== December 13, 2021, Monday at 4pm in B239, [] () ==
 
(reserved by the hiring committee)
 
== December 15, 2021, Wednesday at 4pm in B239, [https://people.seas.harvard.edu/~chr/ Chris Rycroft] (Harvard) ==
 
(reserved by the hiring committee)
 
== December 17, 2021, Friday at 4pm in B239, [] () ==
 
(reserved by the hiring committee)
 
 
 
 
== Future ==
 
[[Colloquia/Spring2022|Spring 2022]]
 
== Past Colloquia ==


[[Colloquia/Spring2021|Spring 2021]]
[[Colloquia/Spring2021|Spring 2021]]

Latest revision as of 15:52, 20 September 2023


UW Madison mathematics Colloquium is on Fridays at 4:00 pm 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
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) 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) 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=25269"