Date: Oct 21, 2013
Speaker: Clayton Petsche, OSU
Abstract: The Dynamical Mordell-Lang Problem combines dynamical systems, algebraic geometry, and number theory in interesting and exciting new ways. One starts in the simple setting of a map from a algebraic variety to itself; for example, one might consider a polynomial function from Euclidean n-space to Euclidean n-space. The goal is to find a simple law or pattern governing the distribution, in the Zariski topology, of forward orbits of points with respect to this map. The problem in full generality is still very much open, but we will survey interesting partial results, and we will give a new result whose proof combines methods from ergodic theory as well as the theory of Berkovich analytic spaces.