Michael Brannan, Texas A&M University
"Quantum symmetries of graphs"
Given a finite graph X, a fundamental question that one can ask about the structure of X is: "What are its symmetries?" Most of the time, when we think of symmetries of X, we think of the usual automorphism group of X. In this talk, I will describe a more general notion of symmetry of graphs, called quantum symmetries. Quantum symmetries of graphs arise quite naturally from the perspective of non-commutative geometry, and are encoded by a certain universal Hopf algebra (i.e., quantum group) co-acting on the algebra of functions on the vertex set of the graph. My goal in this talk will be to give a light introduction to all of these objects, and to explain why they are interesting from a variety of mathematical perspectives (e.g., representation theory, quantum information theory, and operator algebras).
A post-colloquium meet and greet will be held at 2:00 pm using the same Zoom meeting link.