QM Research Seminar: Topological order enriched by non-invertible symmetry

Speaker: Clement Delcamp (​IHES).

I will use finite group topological lattice gauge theory as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order, there is an established axiomatisation in terms of a G-crossed braided fusion categories. I will lay the foundations to generalise this framework using  hypergroup-graded extensions and Hopf monads. Finally, I will construct explicit examples by condensing algebras of charges within a parent topological lattice gauge theory.