Winnie.Li

Affiliation: Penn State University

Title Of Talk: Various aspects of hypergeometric functions

Abstract: The classical hypergeometric functions are studied from analytic viewpoint, as solutions to linear differential equations. The focus of this talk is the algebraic aspect, as hypergeometric Galois representations introduced by Katz. These Galois representations have their Frobenius traces given by hypergeometric character sums, which are finite field analog of the classical hypergeometric functions. Furthermore, since the Katz representations are geometric, they are expected to be automorphic by Langlands philosophy. We'll explain algebraic and geometric properties of hypergeometric character sums, and discuss the automorphy results for low degree hypergeometric Galois representations. This is a joint work with Tong Liu and Ling Long.

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