EVENT DETAILS AND ABSTRACT

Title: The quantitative ergodic theorem and Banach spaces embeddings of the Heisenberg group
Speaker: Tim Austin
Speaker Info: Brown University
Brief Description:
Special Note:
Abstract:

The classical Mean Ergodic Theorem asserts convergence of ergodic averages to some invariant function, but gives no effective control over how fast is this convergence (say, in norm). Quantitative versions of this theorem turn out to be quite subtle: one must search ask instead for long `epochs' of time over which the ergodic averages are approximately constant. I will show an application of these quantitative results to estimating the minimal distortion of the word metric on the discrete Heisenberg group under Lipschitz embeddings into uniformly convex Banach spaces, where one of the quantitative variants of the ergodic theorem gives essentially sharp bounds on the `compression exponent' which quantifies this distortion. Based on joint work with Assaf Naor and Romain Tessera.