Rahim Moosa, Department of Pure Mathematics, University of Waterloo
“A model theory for meromorphic dynamics?”
A rational dynamical system is a pair (X,f) where X is a projective algebraic variety and f is a dominant rational map from X to itself. A meromorphic dynamical system is the generalisation where X is a compact complex manifold and f is a dominant meromorphic self map. The first order theory relevant to the former is the theory ACFA of difference-closed fields; indeed work in this area by Medvedev-Scanlon and Chatzidakis-Hrushovski has lead to significant applications to rational dynamics. This talk is about developing a model theoretic context in which to study the latter: the first order theory CCMA of compact complex manifolds with a generic automorphism. This is work-in-progress with Martin Bays and Martin Hils. The talk will focus on explaining the connection between rational/meromorphic dynamics and model theory.