关于举行杨文元教授（北京大学）学术报告会的通知

报告题目：Conformal density for mapping class groups

报 告人：杨文元教授（北京大学）

报告时间：2022年12月6日（星期二）上午9:30-11:00         

报告地点：zoom 98951767939，密码：GTG

邀 请人：杜晓明副教授

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数学学院

2022年11月29日

报告摘要： In 1976, S. Patterson introduced a class of conformal measures on the limit set of Fuchsian groups, and further developed by D. Sullivan in Kleinian groups with various applications in spectral geometry, Mostow rigidity, geodesic flows and complex dynamics etc. These now called Patterson-Sullivan measures are important instances of conformal density. In this talk, we will explain how to establish a theory of Patterson-Sullivan measures on the Thurston and Gardiner-Masur boundaries for mapping class groups. In particular, the Shadow Lemma and Hopf-Tsuji-Sullivan theorem are obtained for any non-elementary subgroups. Our approach is general and works for any discrete group action on metric spaces with contracting elements.