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Columbia University
Department of Mathematics
JOSEPH FELS RITT LECTURES
Hypergeometric
Functions
The first lecture is an
elementary introduction to multivariate hypergeometric
functions as defined by Gelfand, Kapranov and Zelevinsky in
the 1980's. These special functions appear in many areas of
mathematics, including algebraic geometry, theoretical
physics, combinatorics, and number theory. Our approach is
algorithmic, based on Gröbner deformations of
D-modules. A basic reference is my book with Mutsumi Saito
and Nobuki Takayama, titled "Gröbner
Deformations of Hypergeometric Differential
Equations".
In the second lecture we
examine rational hypergeometric functions,with the goal of
characterizing their denominator polynomials. The proposed
characterization involves discriminants, dual varieties of
toric varieties, and resultants from sparse elimination
theory. This is ongoing joint work with Eduardo Cattani and
Alicia Dickenstein.
Thursday, December 9
Friday, December 10
4:30 p.m.
- BARNARD CAMPUS -
Lehman Auditorium
202 Altschul Hall
Map
to Altschul Hall
Transparencies
for the lectures
(1.2 Mb)
Tea will be served each day at
3:45 p.m.
508 Mathematics
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