Difference between revisions of "Probability Seminar"

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(March 28, Shamgar Gurevitch UW-Madison)
(September 12, 2019, TBA)
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__NOTOC__
 
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= Spring 2019 =
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= Fall 2019 =
  
 
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
 
<b>Thursdays in 901 Van Vleck Hall at 2:25 PM</b>, unless otherwise noted.  
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[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]
 
[mailto:join-probsem@lists.wisc.edu join-probsem@lists.wisc.edu]
  
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== September 5, 2019, TBA ==
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== September 12, 2019, TBA ==
  
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== September 19, 2019, TBA ==
  
== January 31, [https://www.math.princeton.edu/people/oanh-nguyen Oanh Nguyen], [https://www.math.princeton.edu/ Princeton] ==
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<!-- == September 26, 2019, TBA == -->
  
Title: '''Survival and extinction of epidemics on random graphs with general degrees'''
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== October 3, 2019, TBA ==
  
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 $\lambda>0$.
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== October 10, 2019, TBA ==
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] ==
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== October 17, 2019, TBA ==
 
 
Title: '''When particle systems meet PDEs'''
 
 
 
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 7, [http://www.math.cmu.edu/~yug2/ Yu Gu], [https://www.cmu.edu/math/index.html 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, [https://www.math.wisc.edu/~seppalai/ Timo Seppäläinen], UW-Madison==
 
 
 
Title: '''Geometry of the corner growth model'''
 
 
 
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).
 
 
 
== February 21, [https://people.kth.se/~holcomb/ Diane Holcomb], KTH ==
 
 
 
 
 
 
 
 
 
==  <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] ==
 
 
 
 
 
<div style="width:520px;height:50px;border:5px solid black">
 
<b><span style="color:red">&emsp; Please note the unusual day and time.
 
&emsp; </span></b>
 
</div>
 
 
 
== March 7, TBA ==
 
 
 
== 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]==
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== October 24, 2019, TBA ==
  
Title: '''Harmonic Analysis on GLn over finite fields, and Random Walks'''
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== October 31, 2019, TBA ==
  
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'':
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== November 7, 2019, TBA ==
  
$$
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== November 14, 2019, TBA ==
\text{trace}(\rho(g))/\text{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 $GL_n$ over finite fields, and apply the results to random walks. This is joint work with Roger Howe (Yale and Texas AM).
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== November 21, 2019, TBA ==
  
== April 4, TBA ==
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== November 28, 2019, Thanksgiving (no seminar) ==
== 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] ==
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== December 5, 2019, TBA ==
  
== 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 ==
 
  
  
 
<!--
 
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==<span style="color:red"> Friday, August 10, 10am, B239 Van Vleck </span> András Mészáros, Central European University, Budapest ==
 
  
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== <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] ==
  
Title: '''The distribution of sandpile groups of random regular graphs'''
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Title: '''When particle systems meet PDEs'''
  
Abstract:
+
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..
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.
 
  
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== <span style="color:red">'''Tuesday''' </span>, May 7,  Van Vleck 901, 2:25pm, Duncan Dauvergne (Toronto) ==
  
==September 20, [http://math.columbia.edu/~hshen/ Hao Shen], [https://www.math.wisc.edu/ UW-Madison] ==
 
  
Title: '''Stochastic quantization of Yang-Mills'''
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<div style="width:250px;height:50px;border:5px solid black">
 
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<b><span style="color:red">&emsp; Please note the unusual day.
Abstract:
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&emsp; </span></b>
"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.
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</div>
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].
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Title: '''The directed landscape'''
  
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Abstract: I will describe the construction of the full scaling limit of (Brownian) last passage percolation: the directed landscape. The directed landscape can be thought of as a random scale-invariant `directed' metric on the plane, and last passage paths converge to directed geodesics in this metric. The directed landscape is expected to be a universal scaling limit for general last passage and random growth models (i.e. TASEP, the KPZ equation, the longest increasing subsequence in a random permutation). Joint work with Janosch Ormann and Balint Virag.
 
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Revision as of 08:16, 23 May 2019


Fall 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


September 5, 2019, TBA

September 12, 2019, TBA

September 19, 2019, TBA

October 3, 2019, TBA

October 10, 2019, TBA

October 17, 2019, TBA

October 24, 2019, TBA

October 31, 2019, TBA

November 7, 2019, TBA

November 14, 2019, TBA

November 21, 2019, TBA

November 28, 2019, Thanksgiving (no seminar)

December 5, 2019, TBA

Past Seminars