#### Wednesday, March 25, 2015

3:30 pm

Andrew Fiori (Queens) - Rational Conjugacy Classes of maximal Tori in G_2 and F_4

http://www.mast.queensu.ca/~afiori/

In this talk we will discuss the problem of classifying the rational conjugacy classes of maximal tori in groups of type G_2 and F_4 over a field k (of characteristic not 2). We first reduce the classification of maximal tori in these groups to the simpler problems of classifying rational conjugacy classes of subgroups of type A_2 and D_4 respectively, and the study of the rational conjugacy classes of maximal tori in these (more classical) subgroups. We will conclude by describing the structure of the rational tori in those simply connected groups of type D_4 that occur as subgroups of F_4.

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4:30 pm

Vadim Gorin (MIT) - Multilevel Dyson Brownian Motion and its edge limits

http://www.mccme.ru/~vadicgor/

The GUE Tracy-Widom distribution is known to govern the large-time asymptotics for a variety of interacting particle systems on one side, and the asymptotic behavior for largest eigenvalues of random Hermitian matrices on the other side. In my talk I will explain some reasons for this connection between two seemingly unrelated classes of stochastic systems, and how this relation can be extended to general beta random matrices. A multilevel extension of the Dyson Brownian Motion will be the central object in the discussion. (Based on joint papers with Misha Shkolnikov).

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#### Thursday, March 26, 2015

2:00 pm

Agnes Beaudry (UChicago) - The Chromatic Splitting Conjecture at $n=p=2$

Understanding the homotopy groups of the sphere spectrum $S$ is one of the great challenges of homotopy theory. The ring $\pi_*S$ is extremely complex; there is no hope of computing it completely. However, it carries an amazing amount of structure. A famous theorem of Hopkins and Ravenel states that, after localizing at a prime, the sphere spectrum is filtered by ``simpler" spectra called the chromatic layers, which we denote by $L_nS$. How these layers interact with each other is a mystery. A conjecture of Hopkins, the chromatic splitting conjecture, suggests an answer to the problem. The difficulty of the problem grows fast with $n$, and varies with the choice of prime at which we localize. The chromatic splitting conjecture is known to hold in its strongest form at all primes $p$ when $n=1$, and at all odd primes when $n=2$. However, it does not hold when $p=n=2$. In this talk, I explain why it fails in this case.

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4:00 pm

Vadim Gorin (MIT) - Integrable two-dimensional stochastic systems and their asymptotic behavior

http://www.mccme.ru/~vadicgor/

I will speak about a class of probabilistic systems that can be analyzed by essentially algebraic methods. The class includes stepped surfaces, six-vertex model ("square ice"), spectra of random matrices, TASEP-like interacting particle systems, directed polymers in random media, etc. We will discuss the asymptotic behavior of these systems, which is governed by universal limiting objects such as the Gaussian Free Field and Tracy-Widom distributions.

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#### Tuesday, March 31, 2015

2:00 pm

TBA - TBA

3:15 pm

Tea Time

#### Wednesday, April 1, 2015

3:30 pm

Andrew Linshaw (Denver) - T-duality and the chiral de Rham complex

http://web.cs.du.edu/~alinshaw/

T-dual pairs are distinct manifolds equipped with closed 3-forms that admit isomorphism of a number of classical structures including twisted de Rham cohomology, twisted K-theory, and twisted Courant algebroids. An ongoing program is to study T-duality from a loop space perspective; that is, to identify structures attached to the loop spaces that are isomorphic under T-duality. In this talk, I'll explain how the chiral de Rham complex of Malikov, Schechtman, and Vaintrob, gives rise to such structures. This is a joint work with Varghese Mathai (University of Adelaide).

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4:30 pm

Nathan Glatt-Holtz (Virginia Tech) - Stochastic PDEs and Turbulence

http://www.math.vt.edu/people/negh/

I will survey some recent results concerning the ergodic theory of nonlinear stochastic PDEs and describe how these results have bearing on various statistical theories of turbulent fluid flow.

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