Thurston and McMullen rigidity theorems revisited: new proof and generalization

：冀诸超（西湖大学）
：2022-10-11 14:30
：腾讯会议ID：329876227（无密码）

报告人：冀诸超（西湖大学）

时  间：10月11日下午14:30

地  点：腾讯会议ID：329876227（无密码）

内容摘要:

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.

个人简介：

冀诸超，西湖大学理论科学研究员特聘研究员。2020年在法国索邦大学获得博士学位，导师是Romain Dujardin教授。2020-2022在复旦大学上海数学中心做博士后，导师是沈维孝教授。冀诸超的研究方向是复动力系统，以及与算术动力系统，多复变等领域的交叉，在Math. Ann, IMRN等杂志上发表过多篇论文。

 

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