Michael Brannan (University of Waterloo)

Math & Stats Department Colloquium

Friday, October 22nd, 2021

Time: 2:30 p.m.  Place: In-person (Jeffery Hall 234) & Online (via Zoom)

Speaker: Michael Brannan (University of Waterloo)

Title: Quantum symmetries of graphs and non-local games

Abstract: 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, the usual automorphism group of X comes to mind. In this talk, I will describe a more general notion of symmetry of graphs, called quantum symmetries. Quantum symmetries of graphs arise quite naturally within the framework 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. Very recently, quantum symmetries of graphs have also been found to arise within the context of two-player non-local games in quantum information theory. More precisely, they encode winning entangled strategies for the so-called graph isomorphism game. I will give a light introduction to all of these ideas and highlight how tools from non-local games and representation theory combine in a very powerful way to elucidate the structure of graphs, their quantum symmetries, and related operator algebra problems.

Michael Brannan is an Associate Professor in the Department of Pure Mathematics at the University of Waterloo. Before moving to Waterloo in 2021, he was an Associate Professor in the Department of Mathematics at Texas A&M University. He obtained his Ph.D. in Mathematics from Queen's University. He is interested in operator algebras, quantum information theory, representation theory, quantum symmetries, non-commutative probability, quantum algebra, and interactions between these fields.