Lecturer: Laura DeMarco
I will explain connections between complex dynamical systems and arithmetic geometry. I will begin with an introduction to maps on P^1 and their relation to the classical theory of elliptic curves and rational points. It turns out that certain finiteness statements can be deduced from understanding dynamical bifurcations and stability. For higher-dimensional abelian varieties, I will explain some results about maps on P^N and some related open questions in dynamics.
References:
Joseph H. Silverman. The Arithmetic of Dynamical Systems. Springer, Graduate Texts in Mathematics v.241, 2007.