Classification of transitive vertex algebroids

In this dissertation we accomplish the following: · We present a classification of transitive vertex algebroids on a smooth variety X carried out in the spirit of Bressler's classification of Courant algebroids. In particular, we compute the class of the stack of transitive vertex algebroids. · We define deformations of sheaves of twisted chiral differential operators (TCDO) introduced in [AChM] and use the classification result to describe and classify such deformations. As a particular case, we obtain a localization of Wakimoto modules at non-critical level on flag manifolds. · We study representation theory of TCDO and their deformations. In particular, we show an equivalence between certain categories of modules over (deformed) TCDO and categories of twisted D-modules, thus extending a result of [AChM].