Multivariate Hypergeometric Functions

Laura Matusevich, University of Pennsylvania

In the late 1980s, Gelfand, Kapranov and Zelevinsky uncovered a connection between the classical hypergeometric functions and the theory of toric varieties. This surprising link to combinatorics and algebraic geometry can be exploited to obtain hypergeometric results. I will give a small survey of GKZ theory, ending in the recent solution (joint with Ezra Miller and Uli Walther) of a conjecture of Sturmfels concerning holonomic ranks of hypergeometric systems.