Generalized geometric structure in equivariant Poisson geometry

Abstract

In this project we investigate a variety of geometric structures which arise naturally in the study of symmetries in equivariant Poisson geometry and quantization, including: symplectic groupoids and multiplicative Dirac structures, VB-groupoids,VB-algebroids, representations up to homotopy, differentiable stacks and derived symplectic geometry. We propose a program for studying topology and geometry in the context of differentiable stacks, having in mindapplications to the study of singular spaces which appear in Poisson geometry with symmetries, e.g. symplectic orbifolds and Poisson orbifolds. (AU)