The geometry of ∞-categories, Clark Barwick | LMS

Abstract: Higher categories serve lots of purposes in mainstream mathematics. In this talk, I'll describe a construction that takes a suitable geometric object (such as a stratified space or scheme) X and produces an ∞-category that serves as the "stratified homotopy type" of X. I will then explain the sense in which this stratified homotopy type "knows" the constructible sheaves on X and their cohomology. Along the way, we will bear witness to an intimate relationship between certain higher categories and stratified geometry. This is joint work with Saul Glasman and Peter Haine.

This was the supporting lecture at the LMS General Meeting and Hardy Lecture 2025, which took place on 4 July 2025 at De Morgan House, London and online.

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