1% quasimorphisms and group cohomology
7 July 2018 | 9:44 pm

Let , be additive groups (i.e., groups with an abelian addition group law). A map is a homomorphism if one has for all . A map is an affine homomorphism if one has for all additive quadruples in , by which we mean that and . The two notions are closely related; it is easy […]

Heat flow and zeroes of polynomials II: zeroes on a circle
7 June 2018 | 11:15 am

This is a sequel to this previous blog post, in which we discussed the effect of the heat flow evolution on the zeroes of a time-dependent family of polynomials , with a particular focus on the case when the polynomials had real zeroes. Here (inspired by some discussions I had during a recent conference on […]

Commutators close to the identity – an update
30 May 2018 | 4:45 pm

I have just uploaded to the arXiv my paper “Commutators close to the identity“, submitted to the Journal of Operator Theory. This paper resulted from some progress I made on the problem discussed in this previous post. Recall in that post the following result of Popa: if are bounded operators on a Hilbert space whose […]

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