中科院数学与系统科学研究院

数学研究所

综合报告会

报告人：Zlil Sela (The Hebrew University of Jerusalem, Israel)

题  目：On rates of growth in groups

时  间：2024.07.17（星期三）15:30-16:30

地  点：南楼N204

摘  要：A classical result of Jørgensen and Thurston shows that the set of volumes of finite volume complete hyperbolic 3-manifolds is a well-ordered subset of the real numbers of order type $w^w$;. Moreover, they showed that each volume can only be attained by finitely many isometry types of hyperbolic 3-manifolds.We will discuss a group-theoretic analogue of this result: If $\Gamma$ is a non-elementary hyperbolic group, then the set of exponential growth rates of  $\Gamma$ is well-ordered, the order type is at least $w^w$, and each growth rate can only be attained by finitely many finite generating sets (up to automorphisms), and further generalizations of these results.

The talk is intended to be for a wider audience. All the notions that are mentioned in the abstract will be explained. It is based on a joint work with K. Fujiwara (Kyoto University).

简介：Zlil Sela 教授于1991年获得博士学位，现任以色列耶路撒冷希伯来大学教授。他的研究领域是几何群论，解决了Tarski 猜想。他于2002年受邀作ICM 45分钟报告，还获得 Erdos Prize (2003) 及Carol Karp Prize (2008)。