Algebraic Geometry Seminar

Fran├žois LoeserUniversity Pierre and Marie Curie
Motivic curve counting

Wednesday, October 18, 2017 - 1:20pm
Malott 205

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.