中国科学院数学与系统科学研究院

数学研究所

中国科学院华罗庚数学重点实验室

华罗庚青年数学论坛

几何拓扑会议学术报告

报告人：朱晶泽博士（MIT）

题  目： Arnold-Thom conjecture for the arrival time of surfaces

时  间：2024.6.26（星期三） 14:30-15:30

地  点：N913

摘  要：Following Łojasiewicz's uniqueness theorem and Thom's gradient conjecture, Arnold proposed a stronger version about the existence of limit tangents of gradient flow lines for analytic functions. In this talk, I will explain the proof of Łojasiewicz's theorem and Arnold's conjecture in the context of arrival time functions of mean convex mean curvature flows of surfaces. More generally, we prove the conjecture for mean curvature flows starting from two-spheres or generic closed surfaces and mean curvature flows with neck or non-degenerate cylindrical singularities. This is joint work with Tang-Kai Lee.