ONEW on Higher Dirac structures

(1:30-2:00pm GMT)
In this talk, we will discuss holomorphic Dirac-Jacobi structures. They naturally appear in the study of holomorphic Jacobi manifolds. Holomorphic Dirac-Jacobi structures are dissimilar to "real" Dirac structures and their study requires different techniques. We will start by reviewing holomorphic gauge algebroids and holomorphic first jet bundles of holomorphic vector bundles. Then we will introduce holomorphic Courant-Jacobi algebroids and holomorphic Dirac-Jacobi structures before explaining their relationship with generalized contact geometry. Part of this talk is based on a joint work with Luca Vitagliano.

(2:05-2:35pm GMT)
We introduce the notion of a (p,k)-Dirac structurein TM⊕⋀p T*M, where 0≤k≤p-1. The (p,0)-Dirac structures are exactly the higher analogues ofDirac structures of order p introduced by Zambon. The (p,p-1)-Dirac structures are exactly theNambu-Dirac structures introduced by  Hagiwara.In the regular case, such a (p,k)-Dirac structure  is characterized by a characteristic pair.

(2:40-3:10pm GMT)
For every positive integer p, consider the “higher Courant algebroid” TM⊕⋀p T*M. We will make some remarks on its isotropic involutive subbundles (including the Lagrangian ones). Then we show that to any isotropic involutive subbundle one can associate an L∞-algebra of observables
For the special case of closed differential forms, we display an embedding of  these observables that can be interpreted as a prequantization map.

(3:50-4:20pm GMT)
The Severa-Roytenberg correspondence states that degree 2 symplectic Q-manifolds are Courant algebroids. Moreover, it sends Lagrangian Q-submanifolds to Dirac structures.  I will explain how this result extends to higher Courant algebroids and higher Dirac structures. If time permits, I will comment on applications such as reduction, quantization or field theories for higher Courant.