Seminar on Interactive proofs and Connes Embedding, spring 2026

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Time: Thursdays 3:30-5:00
Location: 891 Evans Hall

We will aim to cover the proof of the negative answer to Connes embedding of Ji, Natarajan, Vidick, Wright, and Yuen's via MIP*=RE, incorporating some later simplifications of Lin, de la Salle, Vidick, and others. We will attempt to give a complete proof modulo two results, which are quantum analogues of well known classical theorems of computer science: the anchored parallel repetition theorem for nonlocal games, and the quantum soundness of the low individual degree test.

Schedule:

• Feb 5: Introduction and review of representation theory of finite groups
• Feb 12: Expansion in graphs and the Alon-Roichman theorem. See Launda and Russell (2004) "Random Cayley graphs are expanders: A simple proof of the Alon-Roichman Theorem"
• Feb 19: Stability, the Blum-Luby-Rubinfeld theorem and Gower-Hatami theorem. See Gowers, Hatami (2017) Inverse and stability theorems for approximate representations of finite groups
• Feb 26: The matricial microstates formulation of CEP. Synchonous games and correlations.