Title: G-crossed braided tensor categories and symmetry-enriched topological states of matter
Speaker: Maissam Barkeshli - University of Maryland
Abstract: G-crossed braided tensor categories have recently found applications in the study of quantum many-body states of matter, by providing a mathematical framework to characterize the properties of symmetry defects in a topological quantum state of matter with symmetry group G and in (2+1) space-time dimensions. In this talk, I will begin by reviewing the skeletonization of G-crossed braided tensor categories in terms of a concrete set of data and the relation to symmetry-enriched topological phases of matter. I will then describe a number of recent results regarding (1) how to compute various cohomological obstructions that arise in the theory of G-crossed BTCs, and (2) how to extend the theory to include space-time reflection symmetries. These issues naturally lead to higher categorical structures and also to an understanding of reflection symmetric topological quantum field theories on non-orientable manifolds.