Seminar

To attend this seminar, please register here: https://www.msri.org/seminars/25205

Abstract:

A rational function f(z) is called post-critically finite (PCF) if every critical point is either pre-periodic or periodic. PCF rational functions have been studied for their special dynamics, and their special distribution within the moduli space of all rational maps. By works of W. Thurston and S. Koch, every PCF map (with the exception of flexible Lattès maps) arises as an isolated fixed point of an algebraic dynamical system on the moduli space M_{0,n} of point-configurations on P^1; these dynamical systems are called Hurwitz correspondences.  

I will introduce Hurwitz correspondences and their connection to PCF rational maps, and present a result that relates the complexity of the dynamics of a Hurwitz correspondence with the complexity of the associated PCF rational map.