北航数学论坛学术报告

Marked length spectrum rigidity in groups with contracting elements

杨文元 教授

(北京大学)

时间：2024年11月20日（周三下午）15：30-16：30

地点：沙河校区国实E404

摘要: In this talk, we shall discuss the marked length spectrum rigidity problem in Riemannian geometry from a coarse geometric point of view. Namely, given two cobounded isometric actions of a group G on metric spaces X and Y, the coarse marked length spectrum rigidity asks whether the same length spectrum for the two actions ensures an almost G-equivariant isometry between X and Y. In contrast to the very few known classical rigidity results, we shall establish the coarse version, in a very general setting, for any group actions with contracting property. In addition, we prove a finer marked length spectrum rigidity from confined subgroups and further, geometrically dense subgroups. Our proof is based on the Extension Lemma and uses purely elementary metric geometry. This is joint work with Renxing Wan (ECNU) and Xiaoyu Xu (PKU).

报告人简介: 杨文元，北京大学北京国际数学研究中心博雅特聘教授，博士生导师。主要研究方向是几何群论与低维拓扑，相关研究结果发表在Invent Math, Geometry & Topology, Crelle's journal, Journal of Topology, Math Ann等国际知名期刊。

欢迎大家参加！