Seminar by Zsuzsanna Dancso (Australian National University, Canberra)

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

2014.10.31 | Jane Jamshidi

Date Wed 07 Jan
Time 16:15 17:15
Location Aud.D3 (1531-215)

Abstract: 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.