## Banach and Metric Space Geometry Seminar

**Date:** November 15, 2019

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 220

**Speaker:** Chris Gartland, University of Illinois at Urbana-Champaign

**Title:** *Markov Convexity of Model Filiform Groups*

**Abstract:** The Ribe program is the research program concerned with generalizing local properties of Banach spaces to biLipschitz invariant properties of metric spaces. Among such generalizations that have been found is the notion of Markov p-convexity, proven by Mendel-Naor to generalize uniform p-convexity. One of the first important spaces for which this invariant has been calculated is the Heisenberg group, proven by Li to be Markov p-convex for every p ≥ 4 and not Markov p-convex for any p<4. In this talk, we'll start with background on Carnot groups and model filiform groups - a class of Carnot groups containing the Heisenberg group - and then explain how to use random walks on graphs to compute their Markov convexities.