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Synchronous Games

Hot Topics: MIP* = RE and the Connes’ Embedding Problem October 16, 2023 - October 20, 2023

October 16, 2023 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Vern Paulsen (University of Waterloo)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Synchronous Games


We briefly recall the original statement of the Connes Embedding Problem(CEP), which was in terms of traces, and Kirchberg's equivalent problem about tensor norms on group algebras.

We then introduce synchronous games, synchronous correlations and their connections with traces. This leads to the concept of the fundamental orthogonality relations(FOR) of a synchronous game.

From this viewpoint, MIP*=RE gives a negative answer to the CEP by showing the existence of a FOR that can be realized in a tracial C*-algebra, but not in the algebra considered by Connes.

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Synchronous Games

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