## Algebraic Geometry Seminar

A well-studied question put forward by Manin is that of an asymptotic expansion

for the number of rational/integral points of bounded height. A basic tool in that

study is the height zeta function which is a Dirichlet series. Around 2000, Peyre

suggested to consider the analogous problem over function fields, which has then

an even more geometric flavor since it translates as a problem of enumerative

geometry, namely counting algebraic curves of given degree and establishing

properties of the corresponding generating series.

In this talk I will present joint work with Antoine Chambert-Loir on a geometric

version of a result of Chambert-Loir and Tschinkel on integral points of

bounded height for equivariant compactifications of additive groups. Key use is

made of motivic integrals of Igusa type and of a motivic Poisson formula due

to Hrushovski and Kazhdan. We shall end the talk with some recent results by

Margaret Bilu.