Working Seminar in Groups, Dynamics, and Operator Algebras

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Diego Martinez, Texas A&M University

Title: Amenable traces and quasidiagonality II

Michael Brannan Promotion Talk

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Michael Brannan Promotion Talk, Texas A&M University

Description:

TITLE: Graphs, non-local games, and quantum symmetry groups.

ABSTRACT: A well-known theorem of Lov\'asz says that two finite graphs X and Y are isomorphic if and only if for each graph H, the number of graph homomorphisms from H to X equals the number of graph homomorphisms from H to Y. In this talk, we will consider the following question: What happens if we only ask that the number of homomorphisms from H to X and the number of homomorphisms from H to Y be equal for planar graphs H? I will explain how this planar relaxation of graph isomorphism admits two remarkably different interpretations in terms of (1) the theory of non-local games from quantum information theory, and (2) the algebraic notion of a quantum symmetry group of a graph. I will explain how these two very different perspectives on the same idea can be exploited to construct graphs whose quantum symmetry groups have interesting operator algebraic properties.