Department of

Mathematics


Seminar Calendar
for events the day of Friday, September 26, 2014.

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Friday, September 26, 2014

3:00 pm in 341 Altgeld Hall,Friday, September 26, 2014

Asymptotic expansions in matrix models, topological recursion and applications

Gaetan Borot (Max Planck Institute for Mathematics, Bonn)

Abstract: The talk will be a survey of rigorous results on the all-order asymptotic expansion in matrix models : the existence of a 1/N expansion or oscillatory expansions (established by probabilistic methods), and the topological recursion that govern the combinatorial/algebro-geometric structure of the expansion. I shall describe two applications : (1) the derivation of all-order asymptotic expansions for solutions of the Toda chain and (skew) orthogonal polynomials ; (2) some analyticity results for perturbative knot invariants in Seifert manifolds. This is based on joint works with Guionnet, Kozlowski, and Eynard and Orantin.

4:00 pm in 343 Altgeld Hall,Friday, September 26, 2014

Billey-Postnikov decompositions and rationally smooth Schubert varieties

William Slofstra   [email] (University of California-Davis)

Abstract: A theorem of Ryan and Wolper states that every smooth Schubert variety of type A is an iterated fibre bundle of Grassmannians. I will talk about joint work with Ed Richmond extending this theorem to all finite types. In particular, Ryan and Wolper's theorem is closely related to the combinatorial notion of a Billey-Postnikov decomposition in the Weyl group. Using existence results for Billey-Postnikov decompositions, we also determine all (rationally) smooth Grassmannian Schubert varieties in every type, and apply these results to count the number of smooth Schubert varieties in a full flag variety. Time permitting, I will give an overview of applications of Billey-Postnikov decompositions to inversion hyperplane arrangements, and discuss two important questions for Coxeter groups: when does an element have a Billey-Postnikov decomposition, and what type of Billey-Postnikov decompositions exist?

4:00 pm in 243 Altgeld Hall,Friday, September 26, 2014

$\infty$-categories: $\infty$-abstract! $\infty$-complicated! "$\infty$-confusing ?"

Nima Rasekh (UIUC Math)

Abstract: If you have ever googled a mathematical term then you might have made the mistake of opening the nLab link, which means you were confronted with a lot of confusing long words, most of start with an $\infty$, and you might have asked yourself "What is the point of all those weird words and definitions ?". In this talk, I will try to give one motivation why these kind of definitions might actually have a purpose in the world of topology, generalizing the notion of a fundamental groupoid. Despite the topic, the goal of this talk is very modest and so no prior knowledge of algebraic topology or category theory is assumed, which means students of all backgrounds are welcome to come.