Categorical quantum symmetries and ribbon tensor 2-categories (Hank Chen)

Orateur : Hank Chen

Lieu : salle des Séminaires M3

Résumé :

Procedures for producing 3d topological invariants from algebraic categorical data are well-known; they now come under the name of "topological quantum field theories" (TQFTs). To lift these techniques to higher-dimensions, one performs a categorification, but this program still faces many unknowns. In particular, the central notion of a modular tensor 2-category is an important topic of recent research. In this talk, I will introduce an approach to this problem inspired from derived higher-gauge theory in 4-dimensions. The strategy is to systematically examine the various structures induced on the 2-category of 2-representations of a so-called "cobraided dagger Hopf category". By walking through the interaction of the braiding with the different levels of duality, we can algebraically and geometrically tease out properties of the 2-ribbon structure necessary for describing framed invariants of knots and surfaces in 4-space. This is based on my recent work arxiv:2501.08041.