Palestra: Modular Tensor Categories and Riemann Surfaces
Palestrante: Jethro van Ekeren (UFF)
Data: 24/04/2019 (quarta-feira)
Resumo: Two of the key notions to arise from the synthesis of Lie theory, quantum field theory and low dimensional topology of the 1980-1990s were the notions of vertex algebra (VA) and modular tensor category (MTC). Morphisms in an MTC are naturally describable by a sort of braid notation, and this makes MTCs a source of knot invariants like the Jones polynomial. Following ideas from physics, a vertex algebra V can be used to produce a certain coherent assignment of vector spaces (called conformal blocks) to Riemann surfaces. This data in turn can be used to endow the category of V-modules with the structure of an MTC. In this talk I would like to give an introductory overview of these constructions, with examples, and finally to announce some recent work with T. Arakawa in which we construct an apparently new class of MTCs as categories of representations of subregular affine W-algebras.