Length functions on groups and applications to actions on Gromov hyperbolic spaces

Speaker:Shengkui Ye (NYU Shanghai)

Date:July 6 Tue. 3:00pm -- 4:30 pm

Venue:Lecture Hall, Institute for Advanced Study in Mathematics, No.7 teaching building

Abstract:A length function I 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.