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There are many cooperative games which can be won with higher probability if the players are able to access quantum resources. In fact for some games, the players can have very small probability of winning with classical strategies, but the game can be won with probability one with quantum assistance.

The theory of these games has recently been used to solve the Connes Embedding Problem, which had been open since the 1970's, and has been used to show that the mathematical models for describing quantum correlations are all different.

In this talk we introduce these ideas and focus on the family of synchronous games. For synchronous games there is an algebra whose representation theory determines whether or not they can be won with probability one.

This talk will be accessible to anyone with a basic knowledge of operators on a Hilbert space.