# Geometric Analysis and Topology Seminar

#### Conformal dimensions in probability and analysis

**Speaker:**
Mathav Murugan, University of British Columbia

**Location:**
Warren Weaver Hall 1302 (Note the nonstandard location)

**Date:**
Friday, October 6, 2023, 11 a.m.

**Synopsis:**

Quasisymmetric maps are a metric space analogue of conformal maps. The conformal dimension of a metric space is the infimum of the Hausdorff dimension among all metric spaces that are quasisymmetric to the given space. Conformal dimension was introduced by Pansu (1989) to study boundaries of Gromov hyperbolic spaces. More recently, the notion of conformal walk dimension was introduced to study Harnack inequalities for symmetric diffusion processes. An important application of conformal walk dimension is a generalization of Moser's stability result for Harnack inequality in the Euclidean space to manifolds and more generally spaces equipped with symmetric diffusions. This talk will survey aspects of conformal dimensions in analysis and probability highlighting some parallels and differences.

**Notes:**

Joint with probability seminar. The first 45 minutes of the talk will be suitable for general audience in geometry and probability. The second 45 minutes will aim at people with some prior familarity with the topic.