题目：Totally ramified rational functions - Speiser's graph, dessins d'enfants, existence, classification, and dynamics
时间：2023年11月20日 15：00:00-16:00
地点：数学院425
报告人：胡骏教授
邀请人：肖映青
摘要: A rational function f (viewed as a map from the Riemann sphere to itself) is said to be totally ramified if for every critical value q, every
preimage of q under f is a critical point. We will first give a result on what dynamical pattern of rational map is absent for such rational maps.
Then we introduce Speiser's graphs or apply dessins d'enfants to classify all regular ramified rational maps. Thirdly, we use Speiser's graphs to
show the existence of totally ramified but not regularly ramified rational maps for any degree bigger than 6. Exact formulas of such maps for degree
7 or 8 will be presented. If time is allowed, I will present some partial results on classifying totally ramified but not regularly ramified rational
maps. Some of these are joint works with Weiwei Cui or Yingqing Xiao.
报告人简介：胡骏教授师从Dennis Sullivan教授， 美国纽约城市大学教授，主要的研究领域是低维动力系统和黎曼曲面上不同复结构组成的Teichmuller空间的不同描述。
发表论文近40篇。美国自然科学基金数学博士后基金获得者。曾是加州伯克来大学数学研究所，法国高等学术研究所，马里兰大学帕克分校，新泽西州立罗格斯大学纽瓦克
分校，纽约州立大学石溪分校和上海纽约大学的访问学者或访问教授。
