Research Seminar in Mathematics (MTH G450 - 30757)
Organized by Professor Jonathan Weitsman
Guest Speaker: Dror Bar Natan
University of Toronto
Title: Disorganized Tidbits: Kashiwara-Vergne, Dringel'd, Alekseev-Torossian, Alexander, Virtual knots, and Etingof-Kazhdan
Date: Tuesday, October 28, 2008
Time: 1:00 p.m.
Location: 509 Lake Hall
Abstract: There is compelling evidence including some long-route indirect proofs, that the following are the same, or at least closely and directly related to each other:
The Kashiwara-Vergne conjecture, which says, more or less, that convolutions of Ad-invariant functions on a Lie group are the same as convolutions of Ad-invariant functions on its Lie algebra.
Drinfel'd associators, at least "restricted to one loop", and the work of Alekseev and Torossian.
Knot invariants, and in particular, the multi-variable Alexander polynomial.
Virtual knots in which overcrossings (but not undercrossings) are made to commute.
The Etingof-Kazhdan formalism in the case of co-commutative Lie bi-algebras.
There is also some weaker evidence that all these topics remain related even when the various commutativity, co-commutativity and other restrictions are dropped.
If all goes well, in 5-10 years I will be able to give a coherent explanation of all that (perhaps sooner, if others will get interested and do the work). For now, all I have are some disorganized tidbits.
Partially I will follow the topics and handouts of several talks that I gave recently. In particular, with base:= http://www.math.toronto.edu/~drorbn/Talks, see base/Aarhus-0706 , base/Hanoi-0708 , base/MSRI-0808 , base/Sandbjerg-0810 .
Break 2:00 p.m. - 2:30 p.m.
Department tea, 3:30 p.m. - 4:00 p.m.
Discussion at 5:00 p.m. followed by dinner with the speaker.
Previous Talks:
Fall 2008:9/16, 9/23, 10/07
Started: 23 September 2008 Last modified: 17 October 2008
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