Time：16:00-17:00, Friday, Oct 14, 2022
Venue: Room E4-233, Yungu Campus, Westlake University
Host: Dr. Lifan Guan, Institute for Theoretical Sciences, Westlake University
Speaker：Dr. Zhuchao Ji, Institute for Theoretical Sciences, Westlake University
Title：Thurston and McMullen rigidity theorems revisited: new proof and generalization
Abstract：This is a joint work with Junyi Xie. In 1987, McMullen proved a remarkable rigidity theorem which asserts that aside from the flexible Lattès family, the multiplier spectrum of periodic points determines the conjugacy class of rational maps up to finitely many choices. The proof relies on Thurston's rigidity theorem for post-critically finite maps, in where Teichmüller theory is an essential tool. In this talk we give a new proof of McMullen's theorem without using quasiconformal maps or Teichmüller theory. We also show that aside from the flexible Lattès family, the length spectrum of periodic points determines the conjugacy class of rational maps up to finitely many choices. This generalize the aforementioned McMullen's theorem.
