Past lectures

Abstract

This course will begin with basic notions and techniques to the theory of differential stacks and gerbes. These include groupoid fibrations, stacks, Lie groupoids and Lie algebroids, torsors for Lie groupoids, generalized morphisms of groupoids, Morita equivalence, cohomology theory, S1-central extensions, and S1-gerbes and Dixmier-Douady classes. Several more advanced applications will be covered, including quasi-symplectic groupoids and their relation with momentum map theo- ries, and prequantization of the quasi-Hamiltonian G-spaces. Also, applications to twisted K-theory of stacks, Chern-Connes character, twisted equivariant cohomol- ogy and noncommutative geometry will be covered.