### Comparing word length with displacement for actions on CAT(-1) spaces

Ergodic Theory and Dynamical Systems Seminar

6th December 2018, 2:00 pm – 3:00 pm

Howard House, 4th Floor Seminar Room

Suppose a hyperbolic group G acts sufficiently nicely on a complete CAT(-1) geodesic metric space X. Fix an origin for X and a generating set for G. Each group element, g in G, displaces the origin by a distance comparable to its word length. In this talk we discuss various ways in which we can make an averaged comparison between the word length and displacement associated to the action of G on X. We will also discuss other geometrically interesting real valued functions on hyperbolic groups, for which these comparison results apply.

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