Groups and Operator Algebras Seminar

Speaker: Forrest Glebe (Purdue University)

Title: Kazhdan's Winding Number Argument and 2-Homology

Abstract: In 1983 Voiculescu came up with an example of a sequence of pairs of unitary matrices that commute asymptotically in operator norm but remain far, in operator norm, from any commuting pair of unitaries. An elegant proof, called the "winding number argument," that these matrices are far from commuting matrices was developed by Kazhdan and independently by Excel and Loring. More generally, the argument may be used to show that a function from a group to matrices that is "almost multiplicative" (in the point operator norm topology) is "far" from a genuine representation. In this talk, I explain how to reinterpret this argument as a pairing between an almost representation and 2-homology class of the group. I will explain how this interpretation has led to a systematic way of making almost representations that are far from genuine representations and showing that finitely generated nilpotent groups are stable in the Frobenius norm if and only if they are virtually cyclic.

Zoom link: https://ucph-ku.zoom.us/j/63538748485?pwd=MS9HdGgyS2NQc1p5V3pGbm1SL2VnQT09

Meeting ID: 635 3874 8485. Passcode: 587786

GOA website: https://sites.google.com/view/copenhagen-goa-seminar/home