Pacific Institute for the Mathematical Sciences Colloquium: "What are Hypergeometric Functions"

Abstract

Abstract: Hypergeometric functions occur in many shapes and flavours throughout mathematics and mathematical physics. The first such functions were introduced by Euler and studied in depth by Gauss. Since the end of the 19th the concept of hypergeometric functions was extended in many directions, thus creating a veritable zoo of different functions both inone variable and several variables. By the end of the 1980's Gel'fand, Kapranov and Zelevinsky introduced the concept of A-hypergeometric functions,which created a remarkable amount of order through combinatorial ideas. In this lecture we give a first introduction to hypergeometric functions and explain the idea of A-hypergeometric functions.