Professor Sergei Gukov, Caltech – Geometric Methods in Representative Theory Seminar + Physically Inspired Seminar

Title: “Hidden algebraic structures in topology”

Abstract: The goal of this talk is to give an exposition, from several different angles, of new connections that seem to emerge between low-dimensional topology and abstract algebra. While the general picture for such connections — which will be presented toward the end — is rooted in physics, each particular connection can be formulated as a concrete and verifiable statement or, in some cases, even as a theorem. For example, we will see how Kirby moves of 4-manifolds can be realized as equivalences of vertex operator algebras, some of which were known previously and some are new. In the opposite direction, we will see how starting with purely algebraic questions that involve, say, classification of modular tensor categories and the Witt group, we will be naturally led to questions in topology of 3-manifolds and smooth 4-manifolds.