# 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.