Tangent (co)homology, Duflo isomorphism, and a conjecture of Caldararu

Abstract:

In late '70 Michel Duflo proved that one can twist the PBW isomorphism in Lie theory so that it restricts to an algebra isomorphism on invariants. There exists an analogous result for complex manifolds, stating that the HKR isomorphism can be twisted by an appropriate element so that it induces an algebra isomorphism in cohomology. The main goal of this talk is to present this result together with its homological version, known as Caldararu's conjecture. We will also try to catch a few ingredients of the proof. The talk will be based on joint works with Michel Van den Bergh and Carlo A. Rossi.