Baker-DeMarco Learning Seminar

David Urbanik, Department of Pure Mathematics, University of Waterloo

"The Role of Potential Theory in the Work of Baker-DeMarco"

In their study of preperiodic points of rational maps, Baker and DeMarco use results from Complex Potential Theory and its analogue on Berkovich spaces. The idea is that each preperiodic point determines a measure supported on the boundary of an analogue of the Mandlebrot set, and by comparing the measures arising from two different preperiodic points one can determine if their Mandlebrot-set analogues are equal. Understanding these measures requires tools from Complex Potential Theory and its Berkovich space analogue, and we discuss these tools and their connection to the main theorem in this talk.

MC 5403