URegina-PIMS Distinguished Lecture: Marco Gualtieri

Generalized geometry, introduced by Hitchin in the early 2000s, has not only grown into a formalism for understanding previously mysterious constructions in physics (especially in supersymmetric sigma models) but has also led to the discovery of new mathematical structures such as generalized complex manifolds, generalized Riemannian and Kahler structures, and many other extensions of classical geometric structures such as G2 structures. One of the themes underlying these developments, which originates in the ideas of the Weinstein school of Poisson geometry, is the appearance of differentiable stacks and shifted symplectic structures on them. I will give an overview of these developments aimed at a general mathematical audience with an interest in geometry.