Counting points of homogeneous varieties over finite fields

by Prof. Michel Brion (Institute Fourier, France)

Thursday 2 Feb 2012, 16:00 → 17:00 Asia/Kolkata

AG-69 (Colaba Campus)

Given a system of polynomial equations with integer coefficients, one may first reduce it modulo any prime p, and then count the solutions over the prime field F_p and larger finite fields. The talk will present some remarkable properties of the resulting counting function, first for general systems and then for those where the complex solutions form a unique orbit under the action of some algebraic group.