# Porosity and Differentiability

## Gareth Speight

Date: Oct 10, 2013, time: 14:30

Abstract. A set is porous if arbitrarily close to each point of the set there are holes in the set of radius proportional to their distance away. Porous sets (and their countable unions) give a geometrically interesting class of small sets which have applications in other areas of mathematics.

We discuss two recent applications of porous sets to differentiability problems - generalizations of Rademacher's theorem to Lipschitz functions on infinite dimensional Banach spaces and differentiability of Lipschitz functions inside Lebesgue null subsets of Euclidean spaces.