Vestislav Apostolov will talk in the geometry seminar at 2pm on 22/11/2022. Vesti’s title is “A Calabi type problem in generalized Kahler geometry” and his abstract is below.

*The notion of a generalized Kahler (GK) structure was introduced in the early 2000’s by Hitchin and Gualtieri in order to provide a mathematically rigorous framework of certain nonlinear sigma model theories in physics. Since then, the subject has developed rapidly. It is now realized, thanks to more recent works of Hitchin, Goto, Gualtieri, Bischoff and Zabzine, that GK structures are naturally attached to Kahler manifolds endowed with a holomorphic Poisson structure. Inspired by Calabi’s program in Kahler geometry, which aims at finding a “canonical” Kahler metric in a fixed deRham class, I will present in this talk an approach towards a “generalized Kahler” version of Calabi’s problem motivated by an infinite dimensional moment map formalism, and using the Bismut-Ricci flow introduced by Streets and Tian as analytical tool. As an application, we give a complete description – conjectured by D. Joyce in 1999- of the GK structures of symplectic type on the torus $T^{2n}$. Based on joint works with J. Streets, and with J. Streets and Y. Ustinovskiy.*