Monthly Archives: January 2017

Notes of Claus Koestler’s Cambridge lecture 26-01-2017

An elementary approach to unitary representations of Thompson’s group . Unknown wether amenable or not. Does not contain free subgroups. 1. Sources for unitary representations of 1.1. Traditional approach Characters! Theorem 1 (Gohm-Kostler, Dudko-Madzrodski) Extreme points of the set of … Continue reading

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Notes of Ian Leary’s Cambridge lecture 26-01-2017

Generalizing Bestvina-Brady groups using branched covers Joint with Ignat Soroko and Robert Kropholler. Initial motivation: prove that there exist uncountably many groups of type . 1. Finiteness properties Recall that is type if it has a finite , i.e. it … Continue reading

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Notes of Dima Shlyakhtenko’s Cambridge lecture 25-01-2017

Homology -Betti numbers for subfactors and quasiregular inclusions Joint with Sorin Popa and Stefan Vaes. There were several competing definitions, and they turn out to be equivalent, relief. 1. Betti numbers Associative algebras (and bimodules ) have a Hochschild cohomology … Continue reading

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Notes of Andrei Zuk’s Cambridge lecture 19-01-2017

Random walks on random symmetric groups Joint with Harald Helfgott and Akos Seres. 1. Mixing time Related to expanders: the key word is mixing time. Every finite simple group can be generated by 2 elements. This follows from the classication … Continue reading

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Slides of Pansu’s Cambridge course, lectures 1 to 3, january 2017

Here are the slides of the first 3 lectures, jan. 18th, 25th and feb. 2nd, 2017.

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Notes of Stefan Vaes’ second Cambridge lecture 18-01-2017

Representation theory and cohomology for standard invariants 1. Tube algebra of a quasiregular inclusion The historical reason for the word tube will not appear… Recall that a finite index pair of factors is quasiregular if is spanned by finite index … Continue reading

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Notes of Stefan Vaes 1st Cambridge lecture 17-01-2017

Representation theory and cohomology for standard invariants We study pairs of factors, with finite. There are a bunch of discrete invariants. Standard invariants Rigid algebras Planar algebras (Jones). How can these invariants act on factors ? This is Popa’s theory. … Continue reading

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