Calabi Problem in Generalized Kahler Geometry

Explore a 54-minute lecture on the Calabi problem in generalized Kähler geometry, delivered by Vestislav Apostolov from Université du Québec à Montréal at the University of Miami. Delve into the origins of generalized Kähler structures, introduced by Hitchin and Gualtieri in the early 2000s to provide a geometric framework for nonlinear sigma model theories in physics. Discover how these structures are naturally connected to Kähler manifolds with holomorphic Poisson structures. Learn about Calabi's program in Kähler geometry and its aim to find canonical Kähler metrics in fixed deRham classes. Examine an approach towards a generalized Kähler version of Calabi's problem, inspired by recent works by Goto and Gualtieri and motivated by an infinite dimensional moment map formalism. Gain insights into the resolution of this problem in the case of a toric complex Poisson variety, based on joint work with J. Streets and Y. Ustinovskiy.