EVENT DETAILS AND ABSTRACT

Title: A new type of equidistribution result in non-archimedean dynamics
Speaker: Kenneth Jacobs
Speaker Info: University of Georgia
Brief Description:
Special Note:
Abstract:

Let K be an algebraically closed field that is complete with respect to a non-Archimedean absolute value. We study the dynamics of rational functions with coefficients in K. In this non-Archimedean setting, there is an associated rational map, called the reduction map, which is defined over the residue field of K and carries information about the dynamics. Recently, Rumely introduced a measure nu on the Berkovich line over K that carries information about the reduction of the conjugates of the map. In this talk, we will show that the sequence of measures {nu_n}, associated to the iterates of the map, equidistribute to a natural invariant measure on the Berkovich line. As time permits, we will also discuss recent work of a VIGRE group in which the crucial measures have been shown to give information about the location of the map as a point in moduli space.