Department of

Mathematics

Seminar Calendar
for events the day of Thursday, April 18, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, April 18, 2019

12:00 pm in 243 Altgeld Hall,Thursday, April 18, 2019

Immersions and Laminations on Free Groups

Jean-Pierre Mutanguha (Arkansas Math)

Abstract: Using pullbacks, we proved that mapping tori of graph immersions have word-hyperbolic fundamental groups if and only if they have no Baumslag-Solitar subgroups. We will then use laminations to describe an efficient algorithm that determines whether such groups are word-hyperbolic.

2:00 pm in 347 Altgeld Hall,Thursday, April 18, 2019

Local Limit Theorem (Part 2)

Qiang Wu (UIUC Math)

Abstract: This talk the second part of an introduction to some classical CLT variants, specifically on local limit theorem (LLT). The proof of classical LLT for lattice and non-lattice distribution will be discussed using the characteristic approach. Other various generalizations of LLT will be pointed out. Finally, a concise combinatorial approach for LLT of simple random walk will be sketched. Time permits, I will talk about the generalized Berry-Esseen Inequality.

4:00 pm in 245 Altgeld Hall,Thursday, April 18, 2019

The many aspects of Schubert polynomials

Karola Mészáros (Cornell University)

Abstract: Schubert polynomials, introduced by Lascoux and Schützenberger in 1982, represent cohomology classes of Schubert cycles in flag varieties. While there are a number of combinatorial formulas for Schubert polynomials, their supports have only recently been established and the values of their coefficients are not well understood. We show that the Newton polytope of a Schubert polynomial is a generalized permutahedron and explain how to obtain certain Schubert polynomials as projections of integer point transforms of polytopes. The latter generalizes the well-known relationship between Schur functions and Gelfand-Tsetlin polytopes. We will then turn to the study of the coefficients of Schubert polynomials and show that Schubert polynomials with all coefficients at most $k$, for any positive integer $k$, are closed under pattern containment. We also characterize zero-one Schubert polynomials by a list of twelve avoided patterns. This talk is based on joint works with Alex Fink, Ricky Liu and Avery St. Dizier.