MenuEvents for 04/23/2018 from all calendars
Maxson Lecture Series
Time: 3:00PM - 4:00PM
Location: Blocker 117
Speaker: Fernando Rodriguez-Villegas, The Abdus Salam International Centre for Theoretical Physics
Title: Maxson Lecture I: Hypergeometric functions and L-series
Abstract: The classical one-variable hypergeometric functions nFn-1 with rational parameter has a geometric origin. This means that they arise from a one-parameter family of motives. In particular, for each rational value of the parameter we obtain an L-function of rank n. For example 2F1(1/2,1/2;1,t) corresponds in this way to the Legendre family of elliptic curves Et: y2=x(x-1)(x-t). For each rational number t≠0,1 the rank 2 L-function is that of Et.
Hypergeometric motives represent a class of motives that is accessible for detail study and still large enough to cover a wide range of features. The talk will focus on the explicit calculation of their L-functions.
Working Seminar in Groups, Dynamics, and Operator Algebras
Time: 3:00PM - 3:50PM
Location: BLOC 506A
Speaker: Xin Ma, Texas A&M University
Title: Paradoxical comparison and pure infiniteness of crossed products II
Geometry Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Shamgar Gurevich, University of Wisconsin
Title: A look on Representations of SL(2,q) through the Lens of Size
Abstract: How to study a nice function f of the real line? A physically motivated technique (called Harmonic analysis/Fourier theory) is to expand f in the basis of exponentials (also called frequencies) and study the meaningful terms in the expansion. Now, suppose f lives on a finite non-commutative group G, and is invariant under conjugation. There is a well-known analog of Fourier analysis, using the irreducible characters of G. This can be applied to many functions f that express interesting properties of G. To study f we want to know: Question: Which characters contributes most for the sum? I will describe for you the G=SL(2,Fq) case of the theory we are developing with Roger Howe (Yale/Texas A&M), which attempts to answer the above question. Remark: The irreducible representations of SL(2,Fq) are “well known” for a very long time and are a prototype example in many introductory course on the subject. So, it is nice that we can say something new about them. In particular, it turns out that the representations that people classify as “anomalies” in the old theory are the building blocks of our new theory.
