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The Kashiwara-Vergne problem and flying rings in R^3

Zsuzsanna Dancso
(Australian National University, Canberra)
Onsdag, 7 januar, 2015, at 16:15-17:15, in Aud. D4 (1531-219)
The Kashiwara-Vergne problem is a property of the Baker-Campbell-Haussdorff series which has strong consequences in Lie theory and harmonic analysis. It was conjectured in the 70's and first proven in 2006 by Alekseev and Meinrenken.

I will describe a procedure whose input is a structure in topology (typically some class of knotted objects) and whose output is a set of equations in a graded space. I'll explain how this leads to a one-to-one correspondence between solutions to the Kashiwara-Vergne problem in Lie theory, and certain invariants of a class of knotted tubes in R^4. If time allows, I'll also discuss how this gives rise to a new topological proof of the Kashiwara-Vergne problem, and provides an intuitive explanation for the connection between the Kashiwara-Vergne equations and Drinfel'd associators. This is joint work with Dror Bar-Natan.

Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen