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 __NOTOC__   __NOTOC__ 
   
−  = Fall 2017 =  +  = Spring 2018 = 
   
 <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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 If you would like to sign up for the email list to receive seminar announcements then please send an email to joinprobsem@lists.wisc.edu.   If you would like to sign up for the email list to receive seminar announcements then please send an email to joinprobsem@lists.wisc.edu. 
   
 +  <! == Thursday, January 25, 2017, TBA== > 
   
−  == Thursday, September 14, 2017, [https://math.temple.edu/~brider/ Brian Rider] [https://math.temple.edu/ Temple University] ==  +  == Thursday, February 1, 2017, TBA== 
 +  == Thursday, February 8, 2017, [http://www.math.purdue.edu/~peterson/ Jon Peterson], [http://www.math.purdue.edu/ Purdue] == 
   
−  '''A universality result for the random matrix hard edge'''
 +  Title: TBA 
−   +  
−  The hard edge refers to the distribution of the smallest singular value for certain ensembles of random matrices, or, and what is the same, that of the minimal point of a logarithmic gas constrained to the positive half line. For any "inverse temperature" and “quadratic" potential the possible limit laws (as the dimension, or number of particles, tends to infinity) was characterized by Jose Ramirez and myself in terms of the spectrum of a (random) diffusion generator. Here we show this picture persists for more general convex polynomial potentials. Joint work with Patrick Waters.
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−  <! == Thursday, September 21, 2017, TBA==>
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−   +  
−  <! == Thursday, September 28, 2017, TBA ==
 +  
−  == Thursday, October 5, 2017 ==
 +  
−  == Thursday, October 12, 2017 == >
 +  
−  == Thursday, October 19, 2017 [https://sites.google.com/wisc.edu/vjog/ Varun Jog], [https://www.engr.wisc.edu/department/electricalcomputerengineering/ UWMadison ECE] and [https://graingerinstitute.engr.wisc.edu/ Grainger Institute] ==
 +  
−   +  
−  Title: '''Teaching and learning in uncertainty'''  +  
−   +  
−  Abstract:
 +  
−  We investigate a simple model for social learning with two characters: a teacher and a student. The teacher's goal is to teach the student the state of the world <math>\Theta</math>, however, the teacher herself is not certain about <math>\Theta</math> and needs to simultaneously learn it and teach it. We examine several natural strategies the teacher may employ to make the student learn as fast as possible. Our primary technical contribution is analyzing the exact learning rates for these strategies by studying the large deviation properties of the sign of a transient random walk on <math>\mathbb Z</math>.
 +  
−   +  
−  == Thursday, October 26, 2017, [http://www.math.toronto.edu/matetski/ Konstantin Matetski] [https://www.math.toronto.edu/ Toronto] ==
 +  
−   +  
−  Title: '''The KPZ fixed point'''
 +  
   
 Abstract:   Abstract: 
−  The KPZ fixed point is the Markov process at the centre of the KPZ universality class. In the talk we describe the exact solution of the totally asymmetric simple exclusion process, which is one of the models in the KPZ universality class, and provide a description of the KPZ fixed point in the 1:2:3 scaling limit. This is a joint work with Jeremy Quastel and Daniel Remenik.
 
− 
 
−  <!== Thursday, November 2, 2017, TBA ==>
 
− 
 
−  == Thursday, November 9, 2017, Chen Jia, University of Texas at Dallas ==
 
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− 
 
−  '''Mathematical foundation of nonequilibrium fluctuationdissipation theorems and a biological application'''
 
− 
 
−  The fluctuationdissipation theorem (FDT) for equilibrium states is one of the classical results in equilibrium statistical physics. In recent years, many efforts have been devoted to generalizing the classical FDT to systems far from equilibrium. This was considered as one of the most significant progress of nonequilibrium statistical physics over the past two decades. In this talk, I will introduce our recent work on the rigorous mathematical foundation of the nonequilibrium FDTs for inhomogeneous diffusion processes and inhomogeneous continuoustime Markov chains. I will also talk about the application of the nonequilibrium FDTs to a practical biological problem called sensory adaptation.
 
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−  == Thursday, November 16, 2017, [http://louisfan.web.unc.edu/ Louis Fan], [http://www.math.wisc.edu/ UWMadison] ==
 
− 
 
−  Title: '''Stochastic and deterministic spatial models for complex systems'''
 
− 
 
−  Abstract:
 
− 
 
−  Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individualbased models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integraldifferential equations. The challenge, which is fundamental in any multiscale modeling approach for complex systems, is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.
 
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−  In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE, in particular, why naively adding diffusion terms to ordinary differential equations might fail to account for spatial dynamics in population models. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the timeasymptotic properties of certain population dynamics.
 
− 
 
−  == <span style="color:red"> Friday,</span> November 17, 2017, <span style="color:red"> 1pm, Van Vleck B223, </span> [http://math.depaul.edu/kliechty/ Karl Leichty] [https://csh.depaul.edu/academics/mathematicalsciences/Pages/default.aspx DePaul University] ==
 
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−  <div style="width:400px;height:50px;border:5px solid black">
 
−  <b><span style="color:red"> Please note the unusual room, day, and time </span></b>
 
−  </div>
 
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−  Title: '''Nonintersecting Brownian motions on the unit circle'''
 
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−  Abstract:
 
− 
 
−  Nonintersecting Brownian bridges on the unit circle form a determinantal point process whose kernel is expressed in terms of a system of discrete orthogonal polynomials which may be studied using RiemannHilbert techniques. If the Brownian motions have a drift, then the weight of the orthogonal polynomials becomes complex. I will discuss the tacnode and ktacnode processes, which are related to the Painleve II function, as scaling limits of Nonintersecting Brownian motions on the unit circle and will discuss some of the features and difficulties of RiemannHilbert analysis of discrete orthogonal polynomials with varying complex weights.
 
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−  This is joint work with Dong Wang and Robert Buckingham.
 
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−  == Thursday, November 30, 2017, [https://sites.google.com/site/guoxx097/welcome Xiaoqin Guo], [https://www.math.wisc.edu/ UWMadison] ==
 
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−  Title: '''Harnack inequality, homogenization and random walks in a degenerate random environment'''
 
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−  Abstract: Stochastic homogenization studies the effective equations or laws that characterize the large scale phenomena for systems with complicated random dynamics at microscopic levels. In this talk, we explore the relation between stochastic homogenization and a probabilistic model called random motion in a random medium. In particular we focus on dynamics on the integer lattice which is nonreversible in time and defined by a nondivergence form operator which is nonelliptic. A difficulty in studying this problem is that coefficients of the operator are allowed to be zero. Using random walks in random media, we present a Harnack inequality and a quantitative result for homogenization for this random operator. Joint work with N.Berger (TUMunich), M.Cohen (Jerusalem) and J.D. Deuschel (TUBerlin).
 
− 
 
−  <!== Thursday, December 7, 2017, TBA ==
 
   
−  == Thursday, December 14, 2017, TBA ==  +  == Thursday, February 15, 2017, TBA== 
 +  == Thursday, February 22, 2017, TBA== 
 +  == Thursday, March 1, 2017, TBA== 
 +  == Thursday, March 8, 2017, TBA== 
 +  == Thursday, March 15, 2017, TBA== 
 +  == Thursday, March 22, 2017, TBA== 
 +  == Thursday, March 29, 2017, Spring Break == 
 +  == Thursday, April 5, 2017, TBA== 
 +  == Thursday, April 12, 2017, TBA== 
 +  == Thursday, April 19, 2017, TBA== 
 +  == Thursday, April 26, 2017, TBA== 
 +  == Thursday, May 3, 2017, TBA== 
 +  == Thursday, May 10, 2017, TBA== 
   
   