Hypergeometric functions: the GKZ-perspective

Algebra Seminar
Monday, March 2, 2009 - 15:00
1 hour (actually 50 minutes)
Skiles 269
Purdue University
Starting with some classical hypergeometric functions, we explain how to derive their classical univariate differential equations. A severe change of coordinates transforms this ODE into a system of PDE's that has nice geometric aspects. This type of system, called A-hypergeometric, was introduced by Gelfand, Graev, Kapranov and Zelevinsky in about 1985. We explain some basic questions regarding these systems. These are addressed through homology, combinatorics, and toric geometry.