nLab
Kashiwara-Vergne conjecture

Quoting the seminar page,

The Kashiwara-Vergne conjecture is a subtle property of the Campbell-Hausdorff series which implies that the Duflo isomorphism theorem can be extended to the germs of bi-invariant distributions on a Lie group. This problem is related to the combinatorics of multiple zeta values and to the Deligne-Drinfeld conjecture. It is also related to some open questions in deformation quantization. An important corollary of the Kashiwara-Vergne 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 Kashiwara-Vergne problem. Using this framework they showed that solutions of the Kashiwara-Vergne problem are closely related to Drinfeld’s associators. In fact, starting from any Drinfeld associator one can produce a solution of the Kashiwara-Vergne problem.