Department of

Mathematics


Seminar Calendar
for events the day of Thursday, February 25, 2016.

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Thursday, February 25, 2016

11:00 am in 241 Altgeld Hall,Thursday, February 25, 2016

Algebraicity of automorphic representations: The functoriality approach

Wushi Goldring (Washington University in St. Louis)

Abstract: The Langlands correspondence for number fields predicts a precise distinguished subclass of all automorphic representations that should be in correspondence with pure motives (and so also with their various realizations: certain Galois representations, pure Hodge structures, etc.). In particular, many automorphic representations which are initially defined by analytic and/or representation-theoretic means should have deep algebraic properties, the simplest being that their Hecke eigenvalues should be algebraic. In this talk, I will focus on the possibilities and limitations of using Langlands functoriality to prove such algebraicity results. I'll begin by explaining how automorphic representations naturally break-up into several classes, which are motivated by both geometry and representation theory. I will then discuss some general negative results, some positive examples and some open problems about when it is possible to ``move'' from one of these classes to another one by means of functoriality.

12:00 pm in Altgeld Hall 243,Thursday, February 25, 2016

Characterization of Aleksandrov Spaces of Curvature Bounded Above by Means of the Metric Cauchy-Schwarz Inequality; part II

David Berg (UIUC Math)

Abstract: Joint work of I.D.Berg and I.G.Nikolaev. We employ the previously introduced notion of the K-quadrilateral cosine,the cosine under parallel transport in model K-space,denoted by cosqK. In K-space, modulus cosqK bounded by 1 is equivalent to the Cauchy-Schwarz inequality for tangent vectors under parallel transport. Our principal result states that a geodesic space(of diameter bounded by half the hemisphere diameter for positive K) is a catK space if and only if cosqK is bounded by 1. If, in addition, 1 is actually achieved for two directed non-collinear segments, the geodesic span of the two segments is isometric to a section of K-plane. The diameter restriction is significant. This talk will be devoted to illustrating and explaining these results.If there is time, I will give the ideas of the proofs, veiling the difficult computations that arise,especially in the case of nonzero K, in a decent obscurity.

2:00 pm in Altgeld Hall 241,Thursday, February 25, 2016

p-adic valuations of classical sequences (mostly p=2).

Victor Moll (Tulane University)

Abstract: The classical theorem of Legendre on the largest power of a prime p that divides the sequence of factorials motivated us to conduct investigation of this basic question for a variety of classical sequences. The results will be illustrated with polynomial sequences as well as the Stirling numbers. Most of the statements have been verified experimentally and rigorous proofs are waiting to be produced.

2:00 pmThursday, February 25, 2016

Cancelled due to speaker's flight cancellation. Rescheduled for March 10.

Xuwen Chen (University of Rochester)

4:00 pm in 245 Altgeld Hall,Thursday, February 25, 2016

The method of brackets: a formal procedure for integration

Victor Moll (Tulane University)

Abstract: The method of brackets, originally created in the context of definite integrals coming from Feynman diagrams, is a simple set of heuristic rules that reduce the value of an integral over the half-line to the solution of a linear system of equations. It consists of a small set of rules, one of which is related to Ramanujan Master Theorem. A selection of examples illustrating the method Will be given. This is joint work with Lin Jiu, Karen Kohl, Ivan Gonzalez and Chistophe Vignat.