Speaker
Marco Gualtieri, Toronto University
Abstract
Generalized Kahler geometry, first described by physicists in 1984 as a source of N=(2,2) supersymmetric backgrounds, has an intricate Lie-theoretic structure which is analogous to a Lie algebra in comparison to its integrating Lie group. I will describe this global group-like object, which turns out to be a diagram in symplectic double Lie groupoids (2-shifted symplectic stacks with distinguished Lagrangians). Passing from a local to a global understanding of this structure has certain advantages; most importantly, it clarifies the moduli of generalized Kahler metrics and allows us to express the metric locally in terms of a single scalar function (the generalized Kahler potential). In the first talk, I will cover the infinitesimal story, in the second I will describe the global structure in the symplectic type case (following 1804.05412) , and in the third talk, I will detail the double groupoid picture (following 2407.00831).