Speaker: Anton Alekseev (Université de Genève)
Title: Courant algebroids and generating operators
Date: 20/4/2026
Time: 14:00
Web: https://mat.uab.cat/web/gentle/seminar/
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.
Join: https://teams.microsoft.com/meet/384342250086736?p=IQYdNCVhwU5g18nehy
Meeting ID: 384 342 250 086 736
Passcode: 2eF3v9r4
Speaker: Joel Fine (ULB Brussels)
Title: Symplectic Calabi-Yau manifolds, examples, questions and applications
Date: 19/3/2026
Time: 14:00
Web: https://mat.uab.cat/web/gentle/seminar/
Abstract: In the first half of the talk I will explain what symplectic Calabi-Yau manifolds are, describe some open questions about them, and give a way to construct examples. In the second half of the talk I will describe some applications of these examples to the study of minimal surfaces in 4-manifolds and knots in 3-manifolds.
Join: https://teams.microsoft.com/meet/36524315706050?p=FcXL5yEIBj7o6a2ZAH
Meeting ID: 365 243 157 060 50, Passcode: Sq2MN34P.
Speaker: Aldo Witte (U Hamburg)
Title: Self-crossing stable generalized complex structures
Date: 19/2/2026
Time: 14:00
Web: https://mat.uab.cat/web/gentle/seminar/
Abstract: The first example of a manifold which admits a generalized complex structure, but neither a complex or symplectic structure was $3\mathbb{C}P2\#\overline{19 \mathbb{C}P2}$ which was constructed by Cavalcanti and Gualtieri. This structure is a very special example of a GC structure called stable: It has symplectic type outside of a codimension-two embedded submanifold where it has complex type.
Afterwards many more examples where constructed by several authors, many of these manifolds appear as connected sums. However, none of the GC structures on these manifolds appeared via a connected sum procedure. We will remedy this by introducing the notion of a self-crossing stable generalized complex structure: A generalisation of stable generalized complex structures which now degenerate on an immersed submanifold with transverse self-crossings. We will obtain a connected sum procedure for these structures, and a procedure which smoothens the immersed submanifold into an embedded one. In this manner we recover many of the existing examples in the literature as well as some new ones.
If time permits we will also study the relation with toric geometry and T-duality. Joint work with Gil Cavalcanti and Ralph Klaasse.
Join: https://teams.microsoft.com/meet/38114669707998?p=tvlUUlIxx3kpb9Iiqi
Meeting ID: 381 146 697 079 98, Passcode: 6DL2Zk33