Speaker: Gage Hoefer, Dartmouth College

Date: September 23, 2025

Abstract: A non-local game is one in which two players cooperatively try to convince a third party, according to a predetermined strategy, that they possess a piece of information which they may or may not legitimately have. The study of non-local games— rooted in John Bell’s celebrated work from the ‘60’s— has grown significantly over the past few decades, due to their use in showing the benefits and limitations of quantum entanglement. While initially arising in quantum information theory, significant connections over the past decade between games and the theory of operator algebras have been established. For instance: winning strategies for synchronous games (a particular type of non-local game whose question-answer behavior satisfies stronger conditions) are known to arise from tracial states acting on certain finitely generated -algebras, which encode the rules of the game. In many cases, this *-algebra has a representation as a C-algebra acting on some Hilbert space H, and can be realized as a quotient of a compact quantum group; this allows us to use tools from operator algebras and quantum group theory to answer questions arising from non-local games.

In this talk, I will provide a brief introduction to the theory of non-local games and their strategies. After discussing the basics of compact quantum groups, I introduce a non-local game called the hypergraph isomorphism game. I will show that the winning strategies of different types for this game arise from tracial states acting on a universal *-algebra one can associate to the game. I also show how this universal *-algebra acts on compact quantum groups associated to each hypergraph, which captures the behavior of their automorphisms. Time permitting, I will also indicate how these results might be used to identify quantum symmetries of these objects.

This is based on ongoing work with Georgios Baziotis and Alexandros Chatzinikolaou.