Colloquium abstracts

Michel Brion
Institute Fourier, France
February 2, 2012

Counting points of homogeneous varieties over finite fields:  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.