报告题目：Sullivan's dictionary and prime orbit theorems

报告人：李智强 北京大学

报告时间：2024-11-12 下午 16：00-17：00

报告地点：数学楼301室

报告内容简介：The classical theory of holomorphic dynamics includes the theory of Kleinian groups and the iteration theory of rational maps. In the 1980s Sullivan pointed out several analogies between these two subjects. For example, the concept of a Julia set of a rational map corresponds to the concept of a limit set of a Kleinian group, and periodic orbits of a rational map corresponds to closed geodesics. Analogous to Prime Geodesic Theorems in geometry and the Prime Number Theorem in number theory, we establish the first (effective) Prime Orbit Theorems in complex dynamics outside of the uniformly expanding case. This is partially inspired by the work of Oh–Winter on the Prime Orbit Theorem for hyperbolic (i.e. uniformly expanding) rational maps. This is joint with Tianyi Zheng and Juan Rivera-Letelier.

报告人简介：李智强，男，博士毕业于美国加州大学洛杉矶分校，现任北京大学数学科学学院、北京国际数学研究中心研究员。研究方向为动力系统，量度空间几何，复分析。在Comm. Math. Phys., Adv. Math. (5 篇), 和 Math. Ann. 等著名学术期刊发表论文多篇。在Springer出版专著一部。