Dimensions of escaping and recurrent geodesics

Modern Mathematics Lecture Series

Time

Friday, 16:00-17:00

April 25, 2025

Venue

Lecture Hall C548

Shuangqing Complex Building A

清华大学双清综合楼A座C548报告厅

Online

Zoom Meeting ID: 271 534 5558

Passcode: YMSC

Speaker

Wenyuan Yang 杨文元

BICMR

Wenyuan Yang is a Professor at the Beijing International Center for Mathematical Research (BICMR), Peking University. He received his Ph.D. from Université de Lille 1 in 2011 and was a Postdoctoral Researcher at Université Paris-Sud from 2011 to 2013. He then joined Peking University in 2014. His research area is in Geometric Group Theory and Low-Dimensional Topology.

Personal Website: http://faculty.bicmr.pku.edu.cn/~wyang/

About the lecture

Dimensions of escaping and recurrent geodesics

Abstract

In this talk, we investigate the asymptotic behavior of geodesics—such as escaping and recurrent trajectories—on Riemannian manifolds. Recurrent geodesics are characterized by their endpoints in the visual boundary, which correspond to conical limit points for the fundamental group. The Hausdorff dimension of (uniformly) conical points has been extensively studied, beginning with Patterson’s work (1975) on Fuchsian groups, followed by Sullivan (1979) for geometrically finite Kleinian groups, and later Bishop-Jones (1996) for general Kleinian groups. In this talk, we extend these classical results by computing the Hausdorff dimensions of two other key subsets of the limit set: The Myrberg limit set (a distinguished subclass of non-uniformly conical points) and the non-conical limit set. This is based an ongoing joint work with Mahan Mj (TIFR).