## Physics from the Point of View of Geometry

**Date:**
26 - 30 September 2022

**Location: ** University of Oxford

**Event type:**
CRC Workshop

**Organisers: ** Ulrike Tillmann (INI and Oxford) and Mike Hopkins (Harvard)

In the 1980s the symbiosis between mathematics and physics saw a paradigm shift when physical insight led to compelling mathematical conjectures and their proofs in turn brought validation to physical theories that could not be tested through experiments. One such example is Kontsevich’s proof of Witten’s conjecture on KdV hierarchies. Segal’s axiomatisation of conformal field theory (CFT) and the adaptation to topological field theories (TQFT) by Atiyah provided a common language. These basic concepts were taken forward and are at the origin of a number of new research programs in geometry, topology, algebra, and mathematical physics.

One strand, in the hand of topologists, saw the complete computation of invertible TQFTs, the resolution of the cobordism hypothesis, and a computation of invertible topological phases. This also enabled the complete description of semi-simple field theories in dimension two. Other highlights include the computation of the Verlinde algebra of loop groups in terms of equivariant twisted K-theory, establishing the formal relation of closed string theory and open string theory via Hochschild homology, and the development of a far reaching program to construct higher chromatic cohomology theories in terms of higher dimensional TQFTs.

This workshop celebrates the influence of Graeme Segal on these developments. It brings together leading experts working on a variety of different aspects of geometry and physics of conformal and topological field theory.

**Speakers:** David Ben Zvi (Austin), Dan Freed (Austin), Mike Hopkins (Harvard), Maxim Kontsevich (IHES), Claudia Scheimbauer (TU Munich), Constantin Teleman (Berkeley), Ulrike Tillmann (INI, Oxford), Edward Witten (IAS)

**Registration: ** Participation in the workshop is by invitation but additional places are available. To register for the Clay Research Conference or to register interest in a workshop, email Naomi Kraker. Students please also provide a letter of reference from your supervisor.