Dr. Lukas Geyer (Dept. of Mathematical Sciences, MSU)

09/26/2022  4:10pm

Abstract:  Studying iteration of polynomials, rational functions, and transcendental entire and meromorphic functions naturally leads to the definition of Julia sets, invariant subsets of the complex plane on which the dynamics are chaotic. In many cases, these are very complicated fractals, and a natural geometric invariant to study is their Hausdorff dimension. In this talk I will first survey some of the (by now almost classical) techniques and results on Hausdorff dimension of polynomial and rational Julia sets. Finally, I will address the transcendental case and explain some recent joint work with Jack Burkart, as well as some related results and open questions.