Abstract:

Algebraic dynamics is the study of iteration of polynomial or rational functions. This talk focuses on endomorphisms of projective space. Under the action of conjugation by the projective general linear group, we can form a moduli space of dynamical systems of a certain degree. Certain elements in these moduli spaces have non-trivial automorphisms. This is analogous to the elliptic curves with complex multiplication in the moduli space of elliptic curves. We explore connections to these special maps from several perspectives including rational twists, representation theory, invariant theory, finite matrix groups, group cohomology, and the field of moduli versus field of definition problem. We'll finish by sketching a proof of a recent result on the field of moduli problem.

(Reception to precede at 3:30 p.m.)