What is a hypergeometric function?
Eduardo Cattani Hypergeometric functions (series, equations, integrals) are among the most venerable objects in mathematics. Their study goes back more than 200 years to the work of Euler, Gauss, Riemann, Kummer, and many others. They are ubiquitous in mathematical physics as many well-known partial differential equations may be reduced to Gauss’ hypergeometric equation via separation of variables. One of their higher-dimensional generalizations, due to Gel’fand, Kapranov and Zelevinsky has a combinatorial origin and is of great interest in representation theory, algebraic geometry, number theory, and in mirror symmetry. In this talk which will be aimed to first year graduate students I will introduce the basic concepts and indicate some of the beautiful results in this theory.
