Difference between revisions of "Probability Seminar"

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(March 28, Shamgar Gurevitch UW-Madison)
(March 19, 2020, SPRING BREAK)
 
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__NOTOC__
 
__NOTOC__
  
= Spring 2019 =
+
= Spring 2020 =
  
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
+
<b>Thursdays in 901 Van Vleck Hall at 2:30 PM</b>, unless otherwise noted.  
<b>We  usually end for questions at 3:15 PM.</b>
+
<b>We  usually end for questions at 3:20 PM.</b>
  
 
If you would like to sign up for the email list to receive seminar announcements then please send an email to  
 
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]
 
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]
  
 +
 +
== January 23, 2020, [https://www.math.wisc.edu/~seppalai/ Timo Seppalainen] (UW Madison) ==
 +
'''Non-existence of bi-infinite geodesics in the exponential corner growth model
 +
'''
  
 +
Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s.  A non-existence proof  in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in  November 2018. Their proof utilizes estimates from integrable probability.    This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).
  
== January 31, [https://www.math.princeton.edu/people/oanh-nguyen Oanh Nguyen], [https://www.math.princeton.edu/ Princeton] ==
+
== January 30, 2020, [https://www.math.wisc.edu/people/vv-prof-directory Scott Smith] (UW Madison) ==
 +
'''Quasi-linear parabolic equations with singular forcing'''
  
Title: '''Survival and extinction of epidemics on random graphs with general degrees'''
+
The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral.  By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise.  In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise.  The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.
  
Abstract: We establish the necessary and sufficient criterion for the contact process on Galton-Watson trees (resp. random graphs) to exhibit the phase of extinction (resp. short survival). We prove that the survival threshold $\lambda_1$ for a Galton-Watson tree is strictly positive if and only if its offspring distribution has an exponential tail, settling a conjecture by Huang and Durrett. On the random graph with degree distribution $D$, we show that if $D$ has an exponential tail, then for small enough $\lambda$ the contact process with the all-infected initial condition survives for polynomial time with high probability, while for large enough $\lambda$ it runs over exponential time with high probability. When $D$ is subexponential, the contact process typically displays long survival for any fixed $\lambda>0$.
+
In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution.  These are known as quasi-linear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.
Joint work with Shankar Bhamidi, Danny Nam, and Allan Sly.
 
  
== <span style="color:red"> Wednesday, February 6 at 4:00pm in Van Vleck 911</span> , [https://lc-tsai.github.io/ Li-Cheng Tsai], [https://www.columbia.edu/ Columbia University] ==
+
== February 6, 2020, [https://sites.google.com/site/cyleeken/ Cheuk-Yin Lee] (Michigan State) ==
 +
'''Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points'''
  
Title: '''When particle systems meet PDEs'''
+
In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.
  
Abstract: Interacting particle systems are models that involve many randomly evolving agents (i.e., particles). These systems are widely used in describing real-world phenomena. In this talk we will walk through three facets of interacting particle systems, namely the law of large numbers, random fluctuations, and large deviations. Within each facet, I will explain how Partial Differential Equations (PDEs) play a role in understanding the systems..
+
== February 13, 2020, [http://www.jelena-diakonikolas.com/ Jelena Diakonikolas] (UW Madison) ==
 +
''' '''
  
== February 7, [http://www.math.cmu.edu/~yug2/ Yu Gu], [https://www.cmu.edu/math/index.html CMU] ==
+
== February 20, 2020, [https://math.berkeley.edu/~pmwood/ Philip Matchett Wood] (UC Berkeley) ==
 +
''' '''
  
Title: '''Fluctuations of the KPZ equation in d\geq 2 in a weak disorder regime'''
+
== February 27, 2020, No seminar ==
 +
''' '''
  
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.
+
== March 5, 2020, [https://www.ias.edu/scholars/jiaoyang-huang Jiaoyang Huang] (IAS) ==
 +
''' '''
  
== February 14, [https://www.math.wisc.edu/~seppalai/ Timo Seppäläinen], UW-Madison==
+
== March 12, 2020, No seminar ==
 +
''' '''
  
Title: '''Geometry of the corner growth model'''
+
== March 19, 2020, Spring break ==
 +
''' '''
  
Abstract: The corner growth model is a last-passage percolation model of random growth on the square lattice. It lies at the nexus of several branches of mathematics: probability, statistical physics, queueing theory, combinatorics, and integrable systems. It has been studied intensely for almost 40 years. This talk reviews properties of the geodesics, Busemann functions and competition interfaces of the corner growth model, and presents some new qualitative and quantitative results. Based on joint projects with Louis Fan (Indiana), Firas Rassoul-Agha and Chris Janjigian (Utah).
+
== March 26, 2020, [https://math.cornell.edu/philippe-sosoe Philippe Sosoe] (Cornell) ==
 +
''' '''
  
== February 21, [https://people.kth.se/~holcomb/ Diane Holcomb], KTH ==
+
== April 2, 2020, [http://pages.cs.wisc.edu/~tl/ Tianyu Liu] (UW Madison)==
 +
''' '''
  
 +
== April 9, 2020, [http://stanford.edu/~ajdunl2/ Alexander Dunlap] (Stanford) ==
 +
''' '''
  
 +
== April 16, 2020, [https://statistics.wharton.upenn.edu/profile/dingjian/ Jian Ding] (University of Pennsylvania) ==
 +
''' '''
  
 +
== April 22-24, 2020, [http://frg.int-prob.org/ FRG Integrable Probability] meeting ==
  
==  <span style="color:red"> Wednesday, February 27 at 1:10pm</span> [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] ==
+
3-day event in Van Vleck 911
  
 +
== April 23, 2020, [http://www.hairer.org/ Martin Hairer] (Imperial College) ==
  
<div style="width:520px;height:50px;border:5px solid black">
+
[https://www.math.wisc.edu/wiki/index.php/Colloquia Wolfgang Wasow Lecture] at 4pm in Van Vleck 911
<b><span style="color:red">&emsp; Please note the unusual day and time.  
 
&emsp; </span></b>
 
</div>
 
  
== March 7, TBA ==
+
== April 30, 2020, [http://willperkins.org/ Will Perkins] (University of Illinois at Chicago) ==
 +
''' '''
  
== March 14, TBA ==
 
== March 21, Spring Break, No seminar ==
 
  
== March 28, [https://www.math.wisc.edu/~shamgar/ Shamgar Gurevitch] [https://www.math.wisc.edu/ UW-Madison]==
 
  
Title: '''Harmonic Analysis on GLn over finite fields, and Random Walks'''
 
  
Abstract: There are many formulas that express interesting properties of a 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'':
 
  
$$
 
trace(\rho(g))/dim(\rho),
 
$$
 
  
for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant  ''rank''. This talk will discuss the notion of rank for GLn over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).
 
  
== April 4, TBA ==
 
== April 11, [https://sites.google.com/site/ebprocaccia/ Eviatar Procaccia], [http://www.math.tamu.edu/index.html Texas A&M] ==
 
 
== April 18, [https://services.math.duke.edu/~agazzi/index.html Andrea Agazzi], [https://math.duke.edu/ Duke] ==
 
 
== April 25, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==
 
 
== April 26, Colloquium, [https://www.brown.edu/academics/applied-mathematics/kavita-ramanan Kavita Ramanan], [https://www.brown.edu/academics/applied-mathematics/ Brown] ==
 
 
== April 26, TBA ==
 
== May 2, TBA ==
 
 
 
<!--
 
==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==
 
 
 
Title: '''The distribution of sandpile groups of random regular graphs'''
 
 
Abstract:
 
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.
 
 
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.
 
 
 
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==
 
 
Title: '''Stochastic quantization of Yang-Mills'''
 
 
Abstract:
 
"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].
 
 
-->
 
 
== ==
 
  
 
[[Past Seminars]]
 
[[Past Seminars]]

Latest revision as of 09:30, 26 January 2020


Spring 2020

Thursdays in 901 Van Vleck Hall at 2:30 PM, unless otherwise noted. We usually end for questions at 3:20 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 23, 2020, Timo Seppalainen (UW Madison)

Non-existence of bi-infinite geodesics in the exponential corner growth model

Whether bi-infinite geodesics exist has been a significant open problem in first- and last-passage percolation since the mid-80s. A non-existence proof in the case of directed planar last-passage percolation with exponential weights was posted by Basu, Hoffman and Sly in November 2018. Their proof utilizes estimates from integrable probability. This talk describes an independent proof completed 10 months later that relies on couplings, coarse graining, and control of geodesics through planarity and increment-stationary last-passage percolation. Joint work with Marton Balazs and Ofer Busani (Bristol).

January 30, 2020, Scott Smith (UW Madison)

Quasi-linear parabolic equations with singular forcing

The classical solution theory for stochastic ODE's is centered around Ito's stochastic integral. By intertwining ideas from analysis and probability, this approach extends to many PDE's, a canonical example being multiplicative stochastic heat equations driven by space-time white noise. In both the ODE and PDE settings, the solution theory is beyond the scope of classical deterministic theory because of the ambiguity in multiplying a function with a white noise. The theory of rough paths and regularity structures provides a more quantitative understanding of this difficulty, leading to a more refined solution theory which efficiently divides the analytic and probabilistic aspects of the problem, and remarkably, even has an algebraic component.

In this talk, we will discuss a new application of these ideas to stochastic heat equations where the strength of the diffusion is not constant but random, as it depends locally on the solution. These are known as quasi-linear equations. Our main result yields the deterministic side of a solution theory for these PDE's, modulo a suitable renormalization. Along the way, we identify a formally infinite series expansion of the solution which guides our analysis, reveals a nice algebraic structure, and encodes the counter-terms in the PDE. This is joint work with Felix Otto, Jonas Sauer, and Hendrik Weber.

February 6, 2020, Cheuk-Yin Lee (Michigan State)

Sample path properties of stochastic partial differential equations: modulus of continuity and multiple points

In this talk, we will discuss sample path properties of stochastic partial differential equations (SPDEs). We will present a sharp regularity result for the stochastic wave equation driven by an additive Gaussian noise that is white in time and colored in space. We prove the exact modulus of continuity via the property of local nondeterminism. We will also discuss the existence problem for multiple points (or self-intersections) of the sample paths of SPDEs. Our result shows that multiple points do not exist in the critical dimension for a large class of Gaussian random fields including the solution of a linear system of stochastic heat or wave equations.

February 13, 2020, Jelena Diakonikolas (UW Madison)

February 20, 2020, Philip Matchett Wood (UC Berkeley)

February 27, 2020, No seminar

March 5, 2020, Jiaoyang Huang (IAS)

March 12, 2020, No seminar

March 19, 2020, Spring break

March 26, 2020, Philippe Sosoe (Cornell)

April 2, 2020, Tianyu Liu (UW Madison)

April 9, 2020, Alexander Dunlap (Stanford)

April 16, 2020, Jian Ding (University of Pennsylvania)

April 22-24, 2020, FRG Integrable Probability meeting

3-day event in Van Vleck 911

April 23, 2020, Martin Hairer (Imperial College)

Wolfgang Wasow Lecture at 4pm in Van Vleck 911

April 30, 2020, Will Perkins (University of Illinois at Chicago)





Past Seminars