Dr Olga Maleva (Birmingham) - "Differentiability of functions and geometric measure theory"

Abstract

The talk will be devoted to the geometry of sets that capture points of differentiability of Lipschitz functions. It turns out that while some types of null sets can always be avoided by Lipschitz functions there are some on which every Lipschitz function must be differentiable at some point. We will look at how small these sets can be and discuss some recent developments. We will also show how the methods used in the construction of such sets may lead to a solution of a long-standing open problem in the geometric measure theory.