Part 1 - Grothendieck's works on Banach spaces and their surprising recent repercussions

Gilles Pisier
Texas A&M University - College Station

Grothendieck's thesis and the subsequent paper called "Resume de la theorie meetrique des produits tensoriels topologiques" (1956) had a huge impact on the development of Banach space Geometry in the last 50+ years. We will review some of this, mainly concentrating on the result he called the fundamental theorem, now called Grothendieck's theorem or Grothendieck's inequality. We will describe 3 recent major reappearances of this result, one concerning C*-algebras and operator spaces (or non-commutative Banach spaces) in connection with the Connes-Kirchberg embedding problem, another one-following Tsirelson- involving Bell's inequality and the importance of its "violation" in quantum mechanics, and lastly the recent use of Grothendieck's inequality in graph theory and computer science.

Presentation (PDF File)

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