Workshop: Kontsevich formality theory and the Duflo isomorphism
Banach Center, 06-09 April 2009
IntroductionM. Kontsevich proved that every Poisson manifold admits a canonical formal quantisation up to equivalence. This theorem has opened up new horizons in numerous domains of mathematics, namely Lie theory. Indeed, in the particular case where the considered manifold is the dual of a finite dimensionnal Lie algebra Kontsevich shows that the cohomological isomorphism H^\star(g, S(g))\mapsto H^\star(g,U(g)) (induced by the formality) can be identified in degree 0 with the Duflo isomorphism. This Duflo isomorphism can also be viewed as a consequence of the Kashiwara-Vergne conjecture. This conjecture has been a longstanding issue. A proof, based again on Kontsevich methods, has been given by Alekseev and Meinrenken. An alternative proof, based on the the theory of Drinfeld associators, has been recently written by Alekseev and Torossian. The main idea of this proof is to link the solutions of the Kashiwara-Vergne conjecture to the Drinfeld associators.
ProgramIn this workshop, we want to study Kontsevich formality theorem and its application to Duflo isomorphism and the Kashiwara-Vergne conjecture.
ParticipantsThis workshop is addressed to non-specialists in the field who want to learn more about this part of mathematics - either to broaden their mathematical horizon or in relation to their own work.
SupportThe Banach Center can provide accommodation for those who volunteer to give a talk.
OrganisersThis workshop is organised by Emily Burgunder (Warsaw, Poland), Damien Calaque (Lyon, France) and Maria Ronco (Valparaiso, Chile).