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.
