报告人： 杨文元 （北京大学）

时间：2022-12-10  10:50-11:20

地点：腾讯会议：734-737-203  会议密码：221210

视频链接（请仅用于学习回放）：https://disk.pku.edu.cn:443/link/FA6CC06B52512F9BDE7DB2BFAE73ACF2

报告题目: Floyd boundary of groups with applications in random walks

报告摘要: Floyd boundary was introduced by W. Floyd in 1980 to compactify any finitely generated group. In line with Mostow rigidity, Floyd then proved that this boundary recovers the limit set of geometrically finite Kleinian groups via purely group theoretic terms. After the work of Karlsson and Gerasimov, Floyd boundary becomes an important tool in understanding the geometry of relatively hyperbolic groups. Until recently, Floyd boundary found interesting connections and applications in the study of random walks on groups. In this talk, we will discuss the relation with the Martin boundary of random walks, and Hausdorff dimension of the limit sets of branching random walks in Floyd boundary. These are based on joint works with various subsets of Dussaule,  Gehktman, Gerasimov, Potaygailo, and Longmin Wang.

个人简介：

杨文元，本科和硕士毕业于湖南大学，2011年于法国里尔科学技术大学取得博士学位，2011-2013年期间在南巴黎大学从事博士后研究。2014年入职北京大学北京国际数学研究中心，目前任职长聘副教授。曾获海外高层次青年人才计划支持。主要研究方向是几何群论与低维拓扑，已在Invent Math, Geometry & Topology, Crelle's journal, Journal of Topology, Math Ann等国际知名期刊发表论文多篇。