James Robinson (University of Warwick, United Kingdom)

Finite-dimensional sets and the Lang-Plaut problem

Thursday, 26 November 2026, 16:00-17:00 in HG00.062

Abstract

What does it mean for a set to be "finite-dimensional"? There are many definitions of dimension, and one way to distinguish these is to consider how well a finite-dimensional set can be embedded into a finite-dimensional Euclidean space. It is too much to expect to preserve distances between points, but a bi-Lipschitz embedding is perhaps the next best thing. What "dimension" has to be finite for such an embedding to exist? One of the papers in the recent OpenAI "dump" closes off one possible avenue. I will discuss what is currently known (primarily about less regular embeddings), and explain the significance of this recent result.