A Lecture Series on Hypergeometric Functions

UConn Mathematics is honored to host a series of lectures this summer, on the theory of hypergeometric functions.

The series can be accessed through this link (password is “hyper”).

Video recordings can be found at this YouTube playlist.

Prof. Ling Long
Prof. Ling Long

Professor Ling Long (LSU) will be giving a series of (online) lectures on June 29, June 30, July 1 and July 2, 2021. Each day, Professor Long will lecture at 10am US Eastern (lectures each day will be 90 minutes with a break in the middle). Everyone is welcome to attend! More details on how to connect to her lectures will be made available closer to the date.

Title: Hypergeometric Functions, Character Sums and Applications
Speaker: Prof. Ling Long, Louisiana State University
Abstract: Hypergeometric functions form a class of special functions satisfying a lot of symmetries. They are closely related to the arithmetic of one-parameter families of algebraic varieties, such as the Legendre curves. p-adic hypergeometric functions were investigated by Dwork  leading to his fundamental unit root theory. Hypergeometric functions over finite fields were initiated by Katz and Greene, further developments were made in recent years by many authors. In the proposed mini course, we will explore hypergeometric functions over different settings. Applications of the combined perspectives include obtaining character sum identities, computing special L-values of modular forms,  finding and proving supercongruences (influenced by important conjectures of Beukers, Van Hamme, Rodriguez-Villegas, Roberts and Rodriguez-Villegas,  constructing decomposable Galois representations, and computing arithmetic invariance of certain abelian varieties.

The mini-course will consist of 4 lectures, each 90-minute with a short break in the middle.

Lecture notes:

Slides:

Here are a few references about the material Prof. Long will be speaking about: