Title: Quantum graphs, subfactors and tensor categories
| Speaker: | Roberto Hernández Palomares |
| Affiliation: | University of Waterloo |
| Location: | Please contact Sabrina Lato for Zoom link. |
Abstract: Graphs and their noncommutative analogues are interesting objects of study from the perspectives of operator algebras, quantum information and category theory. In this talk we will introduce equivariant graphs with respect to a quantum symmetry along with examples such as classical graphs, Cayley graphs of finite groupoids, and their quantum analogues. We will also see these graphs can be constructed concretely by modeling a quantum vertex set by an inclusion of operator algebras and the quantum edge set by an equivariant endomorphism that is an idempotent with respect to convolution/Schur product. Equipped with this viewpoint and tools from subfactor theory, we will see how to obtain all these idempotents using higher relative commutants and the quantum Fourier transform. Finally, we will state a quantum version of Frucht's Theorem, showing that every quasitriangular finite quantum groupoid arises as certain automorphisms of some categorified graph.