Brett Nasserden, Department of Pure Mathematics, University of Waterloo
"Archimedean and non-Archimedean Mandelbrot Sets"
An important principle in number theory is to study the completions of a number field in a symmetric manner. For example, the idelic formulation of Class Field theory takes into account the Archimedean and non-Archimedean places of a number field. On the other hand, the principle is potentially violated when one applies the analytic methods of potential theory at the Archimedean places of a number field, and non-analytic methods at the non-Archimedean places. In this talk we will explore the use of Berkovich spaces to apply analytic concepts from potential theory at the non-Archimedean places. Specifically, we will discuss generalized Mandelbrot sets in the Archimedean/non-Archimedean settings and show how one may prove similar statements in both cases.
MC 5403