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SUMMARY:Pure Mathematics Seminar: Valerio Capraro
DESCRIPTION:Groups associated to II_1 factors\n\nLet M,N be II_1-factors. We study the set of morphisms from M to Nbarotimes B(H), where H is a separable Hilbert space. We prove that this set has a natural structure of topological commutative semigroup which always satisfies cancellation and then it embeds into its Grothendieck group. We discuss some examples where this group is trivial and others where it is enormous. If N is an ultrapower of a McDuff II_1-factor, we show that this group carries a natural vector space structure and a natural metric. It is, in fact, a Banach space with natural actions of outer automorphism groups. \n\nThe case N=R^omega, an ultrapower of the hyperfinite II_1-factor, is particularly relevant: existence of extreme points of Hom(M,N), seen as a (convex, closed, and bounded) subset of Hom(M,Nbarotimes B(H)), is equivalent to a problem of Sorin Popa concerning existence of embeddings of M into R^omega with factorial commutant.\n\nThis talk is mainly based on the joint paper with Nate Brown "Groups associated to II_1-factors", Journal of Functional Analysis 264 (2013) 493-507.
DTSTART:20140521T150000
DTEND:20140521T160000
LOCATION:A54, Postgraduate Statistics Centre Lecture Theatre
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