Prime geodesic theorem and closed geodesics for large genus
报告人简介
吴云辉教授，于2012年获得美国布朗大学博士学位，曾为美国莱斯大学G.C.Evans讲师，目前为清华大学数学科学系及丘成桐数学科学中心的教授。吴教授的研究领域包括Teichmüller理论和几何。他致力于在这些领域内探索深层次的数学问题，已在多个国际知名期刊如《Inventiones Mathematicae》、《Journal of the European Mathematical Society》，《Journal of Differential Geometry》上发表了多篇学术论文。吴云辉教授在数学界的贡献为Teichmüller理论与几何的发展提供了重要的理论支持和创新视角。
内容简介
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.
