20 Apr 2026, 14:00 CET. Talk by Anton Alexeev.
Abstract: Courant algebroids were defined in 1997 by Liu-Weinstein-Xu. This theory gained momentum in letters of Severa to Weinstein circulated between 1998 and 2001. In 1999, Roytenberg in his PhD thesis gave an interpretation of Courant brackets as derived brackets defined by a certain cubic generating function.
In this talk, I’ll recall an approach to Courant brackets in terms of generating operators. This technique is inspired by the works of Kosmann-Schwarzbach and Roytenberg. Generating operators are similar to Dirac operators, but they square to zero, or to a first order differential operator. Grützmann-Michel-Xu showed that generating operators can be viewed as Weyl quantizations of Roytenberg’s generating functions. One interesting example of this construction is the Kostant’s cubic Dirac operator. The generating operator approach also leads to the theory of pure spinors in the description of Dirac structures.
The talk is based on joint works with Ping Xu, and with Henrique Bursztyn and Eckhard Meinrenken.