Prime geodesic theorem and closed geodesics for large genus
報告人簡介
吳云輝教授，于2012年獲得美國布朗大學博士學位，曾為美國萊斯大學G.C.Evans講師，目前為清華大學數學科學系及丘成桐數學科學中心的教授。吳教授的研究領域包括Teichmüller理論和幾何。他致力于在這些領域內探索深層次的數學問題，已在多個國際知名期刊如《Inventiones Mathematicae》、《Journal of the European Mathematical Society》，《Journal of Differential Geometry》上發表了多篇學術論文。吳云輝教授在數學界的貢獻為Teichmüller理論與幾何的發展提供了重要的理論支持和創新視角。
內容簡介
In this work, we study the Prime Geodesic Theorem for random hyperbolic surfaces. As an application, we show that as the genus g goes to infinity, on a generic hyperbolic surface in the moduli space of Riemann surfaces of genus g, most closed geodesics of length significantly less than $\sqrt{g}$ are simple and non-separating, and most closed geodesics of length significantly greater than $\sqrt{g}$ are non-simple, confirming a conjecture of Lipnowski-Wright. This is a joint work with Yuhao Xue.
