Grothendieck's work on Banach spaces and its surprising current repercussions

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École normale supérieure - PSL

Published on Apr 16, 2018
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Presentation by Gilles Pisier, during the seminar "Grothendieckian Lectures" (2017-2018), organized by Frédéric Jaëck of the mathematics department of the ENS. ► http://savoirs.ens.fr/expose.php?id=3308 Grothendieck's thesis and his subsequent article entitled 'Summary of the Metric Theory of Topological Tensor Products' (1956) had an enormous impact on the development of the geometry of Banach spaces during the last 60 years. We will review this 'Summary' by focusing on the result that Grothendieck himself called the fundamental theorem of the metric theory of tensor products, now called 'Grothendieck's inequality' or 'Grothendieck's theorem'. This result has recently made a rather unexpected appearance in several fields that were a priori very far from Grothendieck's concerns. One is about C*-algebras and operator spaces (or 'non-commutative Banach spaces'), another about Bell's inequalities and their 'violation' in quantum mechanics, and a last one links Grothendieck's constant to the P=NP problem and graph theory. /// ...

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