### David Bate

University of Warwick

Thursday 15 February 2024, 4.00pm – 5.00pm

Lecture Theatre D (Mathematical Institute)

** Geometric measure theory in metric spaces **

Geometric measure theory studies geometric properties of non-smooth sets. The key concept is that of an n-rectifiable set, which can be parametrised by countably many Lipschitz images of n-dimensional Euclidean space. Characterisations of rectifiable subsets of Euclidean space have important consequences in the theory of partial differential equations, harmonic analysis and fractal geometry.

The recent interest in analysis in non-Euclidean metric spaces naturally leads to questions regarding geometric measure theory in this setting. This talk will give an overview of work in this direction. After introducing the necessary background, we will present recent characterisations of rectifiable subsets of an arbitrary metric space in terms of non-linear projections and tangent spaces.

series: Pure Mathematics Colloquium

organiser: Scott Harper