Groupoids and Algebroids in Geometric Analysis

Abstract: I will show with many examples how Lie groupoids and Lie algebroids appear and how they are used in geometric analysis, particularly in index theory (microlocalisation, index formulae, boundary conditions...) for singular manifolds and/or higher situations (foliations, coverings, orbifolds, etc...). No categorical or very abstract terminology will be used and examples will start from scratch!