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−  = Fall 2020 =  +  = Spring 2021 = 
   
 <b>Thursdays in 901 Van Vleck Hall at 2:30 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 3:20 PM.</b>   <b>We usually end for questions at 3:20 PM.</b> 
   
−  <b> IMPORTANT: </b> In Fall 2020 the seminar is being run online. [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM LINK]  +  <b> IMPORTANT: </b> In Spring 2021 the seminar is being run online. [https://uwmadison.zoom.us/j/91828707031?pwd=YUJXMUJkMDlPR0VRdkRCQVJtVndIdz09 ZOOM LINK] 
   
 If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/ggroups.wisc.edu/forum/#!forum/probsem our group].   If you would like to sign up for the email list to receive seminar announcements then please join [https://groups.google.com/a/ggroups.wisc.edu/forum/#!forum/probsem our group]. 
   
−  == September 17, 2020, [https://www.math.tamu.edu/~bhanin/ Boris Hanin] (Princeton and Texas A&M) ==  +  == January 28, 2021, == 
   
−  '''PreTalk: (1:00pm)'''
 
   
−  '''Neural Networks for Probabilists'''
 +  == February 4, 2021, == 
   
−  Deep neural networks are a centerpiece in modern machine learning. They are also fascinating probabilistic models, about which much remains unclear. In this pretalk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical areas in probability and mathematical physics, including random matrix theory, optimal transport, and combinatorics of hyperplane arrangements.
 
   
−  '''Talk: (2:30pm)'''
 +  == February 11, 2021, == 
   
−  '''Effective Theory of Deep Neural Networks'''
 
   
−  Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based on ongoing joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases are exactly solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly wellbehaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has many consequences also for networks during after training, which I will discuss if time permits.
 +  == February 18, 2021, == 
   
−  == September 24, 2020, [https://people.ucd.ie/neil.oconnell Neil O'Connell] (Dublin) ==
 
   
−  '''Some new perspectives on moments of random matrices'''
 +  == February 25, 2021, [https://math.mit.edu/directory/profile.php?pid=2121 Roger Van Peski] (MIT) == 
   
−  The study of `moments' of random matrices (expectations of traces of powers of the matrix) is a rich and interesting subject, with fascinating connections to enumerative geometry, as discovered by Harer and Zagier in the 1980’s. I will give some background on this and then describe some recent work which offers some new perspectives (and new results). This talk is based on joint work with Fabio Deelan Cunden, Francesco Mezzadri and Nick Simm.
 
   
−  == October 1, 2020, [https://marcusmichelen.org/ Marcus Michelen] ([https://mscs.uic.edu/ UIC]) ==
 
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−  '''Roots of random polynomials near the unit circle'''
 
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−  It is a wellknown (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, probabilistic explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.
 
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−  == October 8, 2020, [http://sites.harvard.edu/~sus977/index.html Subhabrata Sen] ([https://statistics.fas.harvard.edu/ Harvard]) ==
 
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−  '''Large deviations for dense random graphs: beyond meanfield'''
 
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−  In a seminal paper, Chatterjee and Varadhan derived an ErdősRényi random graph, viewed as a random graphon. This directly provides LDPs for continuous functionals such as subgraph counts, spectral norms, etc. In contrast, very little is understood about this problem if the underlying random graph is inhomogeneous or constrained.
 
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−  In this talk, we will explore large deviations for dense random graphs, beyond the “meanfield” setting. In particular, we will study large deviations for uniform random graphs with given degrees, and a family of dense block model
 
−  random graphs. We will establish the LDP in each case, and identify the rate function. In the block model setting, we will use this LDP to study the upper tail problem for homomorphism densities of regular subgraphs. Our results establish that this problem exhibits a symmetry/symmetrybreaking transition, similar to one observed for ErdősRényi random graphs.
 
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−  Based on joint works with Christian Borgs, Jennifer Chayes, Souvik Dhara, Julia Gaudio and Samantha Petti.
 
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−  == October 15, 2020, [https://math.cornell.edu/philippesosoe Philippe Sosoe] (Cornell) ==
 
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−  Title: '''TBA'''
 
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−  Abstract: TBA
 
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−  ==October 22, 2020, [http://www.math.toronto.edu/balint/ Balint Virag] (Toronto) ==
 
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−  Title: '''TBA'''
 
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−  Abstract: TBA
 
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−  == November 5, 2020, [http://sayan.web.unc.edu/ Sayan Banerjee] ([https://stator.unc.edu/ UNC at Chapel Hill]) ==
 
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−  Title: '''TBA'''
 
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−  Abstract: TBA
 
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−  == November 12, 2020, [https://cims.nyu.edu/~ajd594/ Alexander Dunlap] ([https://cims.nyu.edu/ NYU Courant Institute]) ==
 
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−  Title: '''TBA'''
 
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−  Abstract: TBA
 
   
   
 [[Past Seminars]]   [[Past Seminars]] 