Geometric measure theory in metric spaces
This talk will give an overview of recent work that generalises results of classical geometric measure theory to arbitrary metric spaces. We will begin with a brief history of analysis on metric spaces, its relationship with differential geometry and the foundational work of Kirchheim on rectifiable subsets of an arbitrary metric space. I will then present new results related to the Besicovitch–Federer projection theorem and the Marstrand–Mattila characterisation of rectifiable sets in terms of tangent spaces. The talk will be self contained and no specialist prior knowledge is required.