Title: Dynamical Arakelov-Green functions in higher dimensions and arithmetic applications
Abstract: This talk will discuss the connection between Arakelov-Green functions and the arithmetic of dynamical systems. For curves, this connection is best known in terms of arithmetic on their Jacobian varieties and the equidistribution of points of small canonical height with respect to rational functions on P^1. For higher dimensional projective spaces, the situation is much more complex and remains relatively uncharted. In this talk, I will discuss how the Fekete-Leja transfinite diameter is a promising avenue for future progress on this issue, allowing for a generalization of Arakelov-Green functions to the higher-dimensional setting that admits similar quantitative bounds.
