Groups and Operator Algebras seminar

Speaker: Marius Junge (University of Illinois at Urbana-Champaign)

Title: A quantum game perspective on commuting contractions versus commuting unitaries

Abstract: We review different extensions of Grothendieck inequalities and a conjecture by Blecher on matrix extensions of Grothendieck's original inequality, and Pisier, Haagerup, Shlyakhtenko's extension. Using ideas from quantum games, we give qualitative bounds showing how much a commuting set of contractions fails to admit a dilation to commuting unitaries, and disprove the open conjectures by Blecher, Shlyakhtenko and Pisier.

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