Algebraic hypergeometric functions

A. DICKENSTEIN

College Station

Conferencia; Frontiers Lectures; 2015

Texas A & M University

A-hypergeometric functions are the (multivalued)holomorphic solutions to the holonomic system of hypergeometric linear partialdifferential equations defined from an integer matrix A and a parameter vector.These systems beautifully generalize to the multidimensional case classicalGauss hypergeometric equation and were proposed by Gelfand, Kapranov andZelevinsky in the late 80´s, integrating tools from algebraic geometry andcombinatorics to the theory. Following joint work with E. Cattani, F. Martinezand F. Rodriguez Villegas, I will describe geometrically defined algebraicA-hypergeometric functions.