Gunther Cornelissen, Dynamical systems and point counting

Gunther Cornelissen, Utrecht University (The Netherlands) will give a talk with title "Dynamical systems and point counting"

Abstract: Counting the points of a curve over finite fields doesn't determine the curve up to isomorphism; this is analogous to the famous fact that you cannot "hear the shape of a drum". I will show how to remedy this by counting points in a weighted way (namely, using abelian L-series). The method of proof is through the theory of dynamical systems, and - curiously - arose from a study of a quantum statistical mechanical system.