# Geometric Analysis and Topology Seminar

#### Poincare Inequalities Via Quantitative Connectivity, and Differentiability in Metric Measure Spaces

**Speaker:**
Sylvester Eriksson-Bique, NYU

**Location:**
Warren Weaver Hall 1314

**Date:**
Wednesday, October 5, 2016, 11 a.m.

**Synopsis:**

The talk will start by discussing some background of Poincare inequalities on metric measure spaces. We will then introduce a new condition that is equivalent to admitting a Poincare inequality. This metric condition is flexible enough to have a number of applications, and we immediately obtain new classes of spaces admitting Poincare inequalities. We also observe a connection to classical analysis on Euclidean space through Orlicz-Poincare inequalities and Muckenhoupt weights.

In the second half of the talk we introduce an asymptotic version of our condition, and explain how it guarantees a new type of rectifiability result in terms of spaces admitting Poincare inequalities. This result is applied to resolve, in a particular context, a conjecture of Cheeger and Kleiner on so called differentiability spaces. The talk should be understandable without particular knowledge of the applications.