The KashiwaraVergne Problem as an Excuse
 PLACE: Surge 277
 TIME: Wednesday 2:103:30PM
TALKS
 March 31 Vasiliy Dolgushev, ``Formulation of the problem. Overview of goals.''
 April 7 Vasiliy Dolgushev, ``Tangential derivations, special derivations,
infinitesimal braids, etc. I''
 April 14 Christopher Rogers, ``Duflo isomorphism theorem.''
 April 21 Vasiliy Dolgushev, ``Tangential derivations, special derivations,
infinitesimal braids, etc. II''
 April 28 Vasiliy Dolgushev, ``KashiwaraVergne Lie algebras and the
GrothendieckTeichmueller Lie algebra.''
 May 5 NO SEMINAR . A proper subset of participants
is visiting Berkeley :(
 May 12 Vasiliy Dolgushev, ``Drinfeld associators, GRT, and the KnizhnikZamolodchikov
connection. I''
 May 19 NO SEMINAR . A proper subset of participants
is visiting Chicago.
 May 26 Vasiliy Dolgushev, ``Drinfeld associators, GRT, and the KnizhnikZamolodchikov
connection. II''
The KashiwaraVergne conjecture is a subtle property of
the CampbellHausdorff series which implies that the Duflo isomorphism
theorem can be extended to the germs of biinvariant distributions
on a Lie group. This problem is related to the combinatorics
of multiple zeta values and to the DeligneDrinfeld conjecture.
It is also related to some open questions in deformation
quantization.
An important corollary of the KashiwaraVergne conjecture
was proved in papers of M. Andler, A. Dvorsky, S. Sahi, and
C. Torossian. For an arbitrary Lie algebra the conjecture was
established by A. Alekseev and E. Meinrenken.
A. Alekseev and C. Torossian built a nice algebraic
framework for the KashiwaraVergne problem. Using this
framework they showed that solutions of the KashiwaraVergne problem
are closely related to Drinfeld's associators. In fact, starting
from any Drinfeld associator one can produce a solution
of the KashiwaraVergne problem.
In our seminar we will talk about the AlekseevTorossian
algebraic framework for the generalized KashiwaraVergne problem,
we will talk about the GrothendieckTeichmueller Lie algebra and
Drinfeld's associators. Finally we will discuss Kontsevich's
graphical calculus and the AlekseevTorossian connection.
The seminar is based on the sequence of
papers

A. Alekseev and E. Meinrenken, On the KashiwaraVergne
conjecture.

A. Alekseev, B. Enriquez, and C. Torossian,
Drinfeld associators, braid groups and explicit solutions
of the KashiwaraVergne equations

A. Alekseev and C. Torossian, The KashiwaraVergne conjecture and
Drinfeld's associators.
 A. Alekseev and C. Torossian,
Kontsevich deformation quantization and flat connections.

M. Andler, A. Dvorsky, and S. Sahi, Kontsevich
quantization and invariant distributions on Lie groups,

M. Andler, S. Sahi, and C. Torossian,
Convolution of invariant distributions: proof of the KashiwaraVergne conjecture,

D. BarNatan, On Associators and the GrothendieckTeichmuller Group I.

V.G. Drinfeld, On quasitriangular quasiHopf algebras and
on a group that is closely connected with Gal(Qbar/Q).
If you are a graduate student and you are taking this
seminar for credit then you need to give at least one talk
or solve a set of homework problems. I am going to post
the homework problems in the middle of the quarter.
Please, email me if you want to give a talk.