Length functions on groups and applications to actions on Gromov hyperbolic spaces
Topics on hyperbolic geometry
Date: from June 20 to July 20
Venue: Lecture Hall, Institute for Advanced Study in Mathematics, No.7 teaching building
[ IASM visitors plan to organize an irregular seminar from June 20 to July 20. We will arrange about eight 1.5-hour introductory talks, on recent topics in hyperbolic geometry (and low-dimensional topology). The purpose of this seminar is to enhance communication and learn advances in the area. ]
Upcoming Seminar：
Date: | July 6 Tue. 3:00pm -- 4:30 pm |
Speaker: | Shengkui Ye (NYU Shanghai) |
Title: | Length functions on groups and applications to actions on Gromov hyperbolic spaces |
Abstract: | A length function l on a group G is a real-valued function that is conjugation-invariant, homogenous, and subadditive with respect to commuting elements. Such length functions exist in many branches of mathematics, mainly as stable word lengths, stable norms, smooth measure-theoretic entropy, translation lengths on CAT(0) spaces and Gromov delta-hyperbolic spaces, stable norms of quasi-cocycles, rotation numbers of circle homeomorphisms, smooth entropy, dynamical degrees of birational maps and so on. In this talk, we will briefly review the properties of length functions and discuss applications to group actions on Gromov hyperbolic spaces. In particular, we will show that any (rough) isometric action of a finite-index subgroup of SL(n,R),n>2, (R is a ring of algebraic integers in a number field) on a Gromov hyperbolic space must have a fixed point in a X or its Gromov boundary. |
Full information about the Seminar can be seen at: http://www.iasm.zju.edu.cn/iasm/2021/0622/c58777a2397709/page.htm