One of the great challenges in mathematical physics is to lay out precise mathematical structures that capture all of the phenomena of quantum field theory. In general, the more symmetry a theory has the easier it is to study. Conformal field theories occupy a Goldilocks-like middle ground where there is enough symmetry to be tractable without losing too much of the flavour of the general case. In this talk I’ll introduce some of the structures which arise when attempting to axiomatise conformal field theories, such as vertex operators, subfactors, invariants of manifolds, and more. I’ll also lay out some of the fundamental challenges which have made the study of quantum field theories so difficult, along with some recent progress addressing these challenges.

Afternoon tea will be provided at 3:30pm