David Bate

Characterising rectifiable metric spaces using tangent spaces

This talk will present a new characterisation of rectifiable subsets of a complete metric space in terms of local approximation, with respect to the Gromov--Hausdorff distance, by finite dimensional Banach spaces. This is a significant generalisation of a theorem of Marstrand and Mattila of classical geometric measure theory.

After a gentle introduction to analysis on metric spaces, this talk will recall the relevant material from classical GMT. We will then present the main ideas and challenges behind the proof of the new theorem.