Manifolds, Homotopy Theory, and related topics

Date: 2 - 6 August 2027

Location: University of Oxford

The study of the homotopy type of diffeomorphism groups of high-dimensional manifolds—equivalently, of moduli spaces of such manifolds—has seen significant progress this century. This progress has come in roughly three strands: (i) cobordism-categorical techniques for manifolds that have “high genus”, (ii) configuration space integrals, and (iii) embedding calculus. These developments involve increasingly sophisticated ideas from homotopy theory, organised using the language of higher category theory. The objective of this workshop is to bring ideas in this direction closer together, to make further progress in the individual strands and arrive at a bigger conjectural picture. 

This workshop is an in-person format of an online-seminar of the same name. In addition to research talks on current developments, the schedule will contain “visionary” talks of a more speculative and conjectural nature.