Yunhe Sheng:   Dirac structures of omni-Lie algebroids

In order to characterize Lie algebroid structures on a vector bundle $E$, Zhuo Chen and Zhangju Liu introduced the notion of omni-Lie algebroids, which is a generlization of Alan Weinstein's omni-Lie algebras. There are three parts in this talk, first I will introduce the notion of omni-Lie algebroids by using the covariant differential operator bundle and the first jet bundle of a vector bundle $E$. Then we study the properties of Dirac structures, in particular, Lie algebroid structures on $E$ correspond to some special Dirac structures of omni-Lie algebroids. At last, I introduce the notion of $E$-Courant algebroids which is a generalization of Courant algebroids introduced by Liu, Weinstein and Xu.