Almost synchronous strategies and von Neumann algebras

par Mikael de la Salle (CNRS, Université Lyon 1)

mardi 6 juin 2023, 14:00 → 15:00 Europe/Paris

Salle du conseil du LIP (3eme étage) (ENS LYON)

If two positive L^2 functions are close in the L^2 norm, then they admit sub-level sets that are also close in measure. This is a very easy exercise. In 1976, Alain Connes adapted this to matrices (and more generally tracial, or type I/II, von Neumann algebras); this was a part of his celebrated work on the classification of injective factors. This influencial inequality was recently used by Thomas Vidick to prove that synchronous games that admit good finite-dimensional strategies also admit good synchronous strategies. I will explain how to extend Connes' inequality to general von Neumann algebra, and how this allows to extend Vidick's reduction to infinite dimension. This is a joint work with Amine Marrakchi.