Title：Growth of finitely generated groups
Speaker：Wenyuan Yang 杨文元 (Peking University)
Abstract: In his 1968 paper, Milnor initiated the study of growth of finitely generated groups, which has continued to be an active research topic nowadays in Geometric Group Theory. The growth function of a finitely generated group counts the number of elements in a growing ball in word metric, reminiscent of the classical lattice counting problem in geometry. In this minicourse, we shall focus on groups with exponential growth function, and study what a generic element looks like when groups have certain coarse negative curvature.
The plan of the minicourse is as follows:
Lecture 1: we introduce the notion of Cayley graph and revisit Milnor's argument, now called Milnor-Svarc Lemma, the fundamental lemma of GGT. The growth classification of finitely generated groups will be described.
Lecture 2: we discuss by examples various classes of negatively curved groups, including (relatively) hyperbolic groups and acylindrically hyperbolic groups. A particular emphasis shall be given to the notion of strongly contracting elements and other invariants.
Lecture 3: we will explain how the contracting property could be useful to study counting problems, such as estimating growth function and understanding generic elements.
Time and venue：
11/13 (Wednesday) 13:30-15:30, Zhizhi Building 22
11/14 (Thursday) 10:00-12:00, Zhizhi Building 22
11/15 (Friday) 10:00-12:00, Zhizhi Building 42
Zoom ID: 989 8689 0777 (password 864691)
About the Speaker: Wenyuan Yang is a Boya Distinguished Professor at Peking University. He graduated from Hunan University with his bachelor's and master's degrees. In 2011, he obtained his PhD from Université Lille 1 Sciences et Technologies. From 2011 to 2013, he conducted postdoctoral research at Université Paris Sud. In 2014, he joined the Beijing International Center for Mathematical Research at Peking University. His main research areas are geometric group theory and low-dimensional topology, and he has published multiple papers in internationally renowned journals such as Invent Math, Geometry & Topology, Crelle's Journal, Journal of Topology, and Math Ann.
报告人简介: 杨文元，北京大学博雅特聘教授、国家级高层次人才。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。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。
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