MenuEvents for 01/22/2020 from all calendars
Number Theory Seminar
Time: 1:45PM - 2:45PM
Location: BLOC 220
Speaker: Alex Dunn, UIUC
Title: Moments of half integral weight modular L-functions, bilinear forms and applications
Abstract: Given a half-integral weight holomorphic newform f, we prove an asymptotic formula for the second moment of the twisted L-function over all primitive characters modulo a prime. In particular, we obtain a power saving error term and our result is unconditional; it does not rely on the Ramanujan-Petersson conjecture for the form f. This gives a very sharp Lindelöf on average result for L-series attached to Hecke eigenforms without an Euler product. The Lindelöf hypothesis for such series was originally conjectured by Hoffstein. In the course of the proof, one must treat a bilinear form in Salié sums. It turns out that such a bilinear form also has several arithmetic applications to equidistribution. These are a series of joint works with Zaharescu and Shparlinski-Zaharescu.
URL: Event link
Noncommutative Geometry Seminar
Time: 2:00PM - 3:00PM
Location: BLOC 628
Speaker: Xin Ma, SUNY Buffalo
Title: The groupoid semigroup and its application
Abstract: In this talk, I will introduce and discuss an algebraic tool called the groupoid semigroup. I will show how this semigroup help establishing the almost unperforation form for dynamical comparison. Then, I will show how it relates to the type semigroup in the ample case. Finally, I will present some result on (strongly) pure infiniteness of reduced groupoid C*-algebras.
Numerical Analysis Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 628
Speaker: Douglas Arnold, University of Minnesota
Title: Complexes from complexes
Abstract: The finite element exterior calculus has highlighted the importance of Hilbert complexes to partial differential equations and their numerical solution. The most canonical and most extensively studied example is the de Rham complex, which is what is required for application to Darcy flow, Maxwell's equations, the Hodge Laplacian, and numerous problems. But there are many other important differential complexes as well, with applications to elasticity, plates, incompressible flow, general relativity, and other areas. These complexes are less well known and in many cases their properties not established. In this talk I will discuss a systematic procedure for deriving such complexes and deriving their crucial properties.
Student/Postdoc Working Geometry Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 624
Speaker: A. Huang, TAMU
Title: Vanishing Hessian, wild forms and their border VSP
Graduate Student Organization Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 628
Speaker: Jacob Mashburn
Title: Non-crossing Partitions and Free Probability Theory
Abstract: In the mid-1980s, Dan Virgil Voiculescu introduced free probability primarily as a tool for solving the free group factor isomorphism problem, but throughout the 1990s, connections were made to random matrix theory, combinatorics, representation theory, classical probability, etc. For the first few years of its existence, results were proven mostly using techniques in operator theory, but in the early 1990s, Roland Speicher provided an alternate proof to Voiculescu's Free Central Limit Theorem using non-crossing partitions, which motivated his later definition of free cumulants (another analogy to classical probability), which plays a crucial role in free probability. I will begin by covering the basics of free probability and noncrossing partitions, then introducing an equivalent definition of free independence in terms of free cumulants. Finally, I will sketch Speicher's proof of the Free Central Limit Theorem. Throughout, comparisons between free and classical probability will be discussed. Thanks to the combinatorial nature of these topics, a background in operator theory (or even analysis more advanced than undergraduate level) is not needed.
