Past Probability Seminars Spring 2020: Difference between revisions

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== Fall 2010 ==
= Spring 2019 =


<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.
<b>We  usually end for questions at 3:15 PM.</b>


Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. If you would like to receive announcements about upcoming seminars, please visit [https://www-old.cae.wisc.edu/mailman/listinfo/apseminar this page] to sign up for the email list.
If you would like to sign up for the email list to receive seminar announcements then please send an email to
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]




[[Past Seminars]]


== January 31, TBA ==
== February 7, [http://www.math.cmu.edu/~yug2/ Yu Gu], [https://www.cmu.edu/math/index.html CMU] ==


==Friday, September 3, 4PM B239 [http://www.math.wisc.edu/~seppalai/ Timo Seppäläinen (UW Madison)]  ([[Colloquia|Math Colloquium]])==
Title: '''Fluctuations of the KPZ equation in d\geq 2 in a weak disorder regime'''
:Title: '''Scaling exponents for a 1+1 dimensional directed polymer'''


:Abstract: Directed polymer in a random environment is a model from statistical physics that has been around for 25 years. It is a type of random walk that evolves in a random potential. This means that the walk lives in a random landscape, some parts of which are favorable and other parts unfavorable to the walk. The objective is to understand the behavior of the walk on large space and time scales.
Abstract: We will discuss some recent work on the Edwards-Wilkinson limit of the KPZ equation with a small coupling constant in d\geq 2.
:I will begin the talk with simple random walk straight from undergraduate probability and explain what diffusive behavior of random walk means and how Brownian motion figures into the picture. The recent result of the talk concerns a particular 1+1 dimensional polymer model: the order of magnitude of the fluctuations of the polymer path is described by the exponent 2/3, in contrast with the exponent 1/2 of diffusive paths. Finding a rigorous proof of this exponent has been an open problem since the introduction of the model.  


== February 14, TBA ==
== February 21, TBA ==
== February 28, TBA ==
== March 7, TBA ==
== March 14, TBA ==
== March 21, Spring Break, No seminar ==


==Thursday, September 16, [http://www.math.wisc.edu/~moreno/ Gregorio Moreno Flores (UW - Madison)]==
== March 28, TBA ==
:Title: '''Asymmetric directed polymers in random environments.'''
== April 4, TBA ==
== April 11, [https://sites.google.com/site/ebprocaccia/ Eviatar Proccia], [http://www.math.tamu.edu/index.html Texas A&M] ==


:Abstract: It is well known that the asymmetric last passage percolation problem can be approximated by a Brownian percolation model, which is itself related to the GUE random matrices. This allows to transfer many results about random matrices to the setting of asymmetric last passage percolation.<br>
== April 18, [https://services.math.duke.edu/~agazzi/index.html Andrea Agazzi], [https://math.duke.edu/ Duke] ==
:In this talk, we will introduce two different schemes to treat asymmetric directed polymers in random environments.


==Thursday, September 30, [http://math.colorado.edu/~brider/ Brian Rider (University of Colorado at Boulder)]==
== April 25, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==
:Title: '''Solvable two-charge models'''


:Abstract: I'll describe recent progress on ensembles of random matrix type which can be viewed as having particles of two distinct "charges", subject to coulombic interaction. The natural (and classic) example is Ginibre's  non-symmetric Gaussian matrix in which the particles (eigenvalues) live in the complex plane. Taking this as a starting point and forcing the particles down to the line produces a family of ensembles which interpolate (though not in the way we might want) between the well studied Gaussian Orthogonal and Symplectic Ensembles.
== April 26, Colloquium, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==


:Joint work with Christopher Sinclair and Yuan Xu (Univ. Oregon).
== April 26, TBA ==
== May 2, TBA ==


==Thursday, October 7, [http://www.math.wisc.edu/~valko/ Benedek Valko (UW - Madison)]==
:Title: '''Scaling limits of tridiagonal matrices'''


:Abstract: I will describe the point process limits of the spectrum for a certain class of tridiagonal matrices. The limiting point process can be defined through a coupled system of stochastic differential equations. I will discuss various applications of this description, e.g. eigenvalue repulsion, probability of large gaps and central limit theorem for the number of points in an interval.
<!--
==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==




:Joint work with E. Kritchevski and B. Virag (Toronto).
Title: '''The distribution of sandpile groups of random regular graphs'''


==Thursday, October 14, [http://www.math.northwestern.edu/mwp/ MIDWEST PROBABILITY COLLOQUIUM], (no seminar)==
Abstract:
<br>
We study the distribution of the sandpile group of random <math>d</math>-regular graphs. For the directed model we prove that it follows the Cohen-Lenstra heuristics, that is, the probability that the <math>p</math>-Sylow subgroup of the sandpile group is a given <math>p</math>-group <math>P</math>, is proportional to <math>|\operatorname{Aut}(P)|^{-1}</math>. For finitely many primes, these events get independent in limit. Similar results hold for undirected random regular graphs, there for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne.


==Thursday, October 21, [http://www.math.wisc.edu/~kuelbs/ Jim Kuelbs (UW - Madison)]==
Our results extends a recent theorem of Huang saying that the adjacency matrices of random <math>d</math>-regular directed graphs are invertible with high probability to the undirected case.
:Title: '''An Empirical Process CLT for Time Dependent Data'''


:Abstract: For stochastic processes <math>\{X_t: t \in E\}</math>, we establish sufficient conditions for the empirical process based on <math>\{ I_{X_t \le y} - P(X_t \le y): t \in E, y \in \mathbb{R}\}</math> to satisfy the CLT uniformly in <math> t \in E, y  \in \mathbb{R}</math>. Corollaries of our main result include examples of classical processes where the CLT holds, and we also show that it fails for Brownian motion tied down at zero and <math>E= [0,1]</math>.


:Joint work with Tom Kurtz and Joel Zinn.
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==


Title: '''Stochastic quantization of Yang-Mills'''


==Thursday, October 28, [http://www.math.toronto.edu/alberts/ Tom Alberts (University of Toronto)]==
Abstract:
:Title: '''TBA'''
"Stochastic quantization” refers to a formulation of quantum field theory as stochastic PDEs. Interesting progress has been made these years in understanding these SPDEs, examples including Phi4 and sine-Gordon. Yang-Mills is a type of quantum field theory which has gauge symmetry, and its stochastic quantization is a Yang-Mills flow perturbed by white noise.
In this talk we start by an Abelian example where we take a symmetry-preserving lattice regularization and study the continuum limit. We will then discuss non-Abelian Yang-Mills theories and introduce a symmetry-breaking smooth regularization and restore the symmetry using a notion of gauge-equivariance. With these results we can construct dynamical Wilson loop and string observables. Based on [S., arXiv:1801.04596] and [Chandra,Hairer,S., work in progress].


==<span style="color:#009000"> Wednesday, November 17, 2:30pm</span>, [http://math.stanford.edu/~pmwood/ Philip Matchett Wood (Stanford)]==
-->
<span style="color:#FF0000">'''NOTE THE UNUSUAL TIME!'''<span style="color:#009000">
:Title: '''Random tridiagonal doubly stochastic matrices'''


:Let <math>T_n</math> be the compact convex set of tridiagonal doubly stochastic
== ==
matrices.  These arise naturally as birth and death chains with a
uniform stationary distribution.  One can think of a ‘typical’ matrix
<math>T_n</math> as one chosen uniformly at random, and this talk will present a
simple algorithm to sample uniformly in <math>T_n</math>.  Once we have our hands
on a 'typical' element of <math>T_n</math>, there are many natural questions to
ask:  What are the eigenvalues? What is the mixing time?  What is the
distribution of the entries?  This talk will explore these and other
questions, with a focus on whether a random element of <math>T_n</math> exhibits
a cutoff in its approach to stationarity.  Joint work with Persi
Diaconis.


==Thursday, November 18, [http://www.math.wisc.edu/~jmiller/ Joseph S. Miller (UW - Madison)]==
[[Past Seminars]]
:Title: '''TBA'''

Revision as of 16:25, 15 January 2019


Spring 2019

Thursdays in 901 Van Vleck Hall at 2:25 PM, unless otherwise noted. We usually end for questions at 3:15 PM.

If you would like to sign up for the email list to receive seminar announcements then please send an email to join-probsem@lists.wisc.edu


January 31, TBA

February 7, Yu Gu, CMU

Title: Fluctuations of the KPZ equation in d\geq 2 in a weak disorder regime

Abstract: We will discuss some recent work on the Edwards-Wilkinson limit of the KPZ equation with a small coupling constant in d\geq 2.

February 14, TBA

February 21, TBA

February 28, TBA

March 7, TBA

March 14, TBA

March 21, Spring Break, No seminar

March 28, TBA

April 4, TBA

April 11, Eviatar Proccia, Texas A&M

April 18, Andrea Agazzi, Duke

April 25, Kavita Ramanan, Brown

April 26, Colloquium, Kavita Ramanan, Brown

April 26, TBA

May 2, TBA

Past Seminars