One of the most exciting consequences of the recent MIP* = RE result by Ji, Natarajan, Vidick, Wright, and Yuen is the resolution of Connes' embedding problem (CEP). Although this problem started out as a casual question about embeddings of von Neumann algebras, it has gained prominence due to its many equivalent and independently interesting formulations in operator theory and beyond. In particular, MIP* = RE resolves the CEP by resolving Tsirelson's problem, an equivalent formulation of CEP involving quantum correlation sets.
In this expository talk, I'll try to explain the connection between MIP* = RE and Connes' original problem directly, using the synchronous algebras of Helton, Meyer, Paulsen, and Satriano. I'll also explain how one of the remaining open problems on the algebraic side, the existence of a non-hyperlinear group, is related to the study of variants of MIP* with lower descriptive complexity.
This talk will be aimed primarily at physicists and computer scientists, although hopefully there will be something for everyone.