Abstract: My research is focused on the existence of special Hermitian metrics on complex manifolds. In this talk, I will introduce some of the basic concepts and objects involved in complex differential geometry: Kahler forms, the Levi-Civita connection, the Ricci form, and the first Chern class. Then, I will give a very quick account of Yau's theorem before pivoting to the problem of how such a result might be generalized to the non-Kahler setting.

Contact person: Ioana Suvaina and Rares Rasdeaconu

Abstract: We will discuss some obstructions to the existence of "Bismut Hermitian-Einstein" metrics, providing counter-examples to a naive generalization of Calabi-Yau metrics. The obstruction will require us to introduce some concepts from generalized complex geometry. These tools will also prove to be very helpful for studying the flow equation. To attempt to overcome these obstructions, we will consider a generalization of the Kahler condition coming out of generalized complex geometry and some Monge-Ampere-type PDEs that arise in the quest for non-Kahler Calabi-Yau metrics in this setting.

Contact person: Ioana Suvaina and Rares Rasdeaconu

Abstract: TBA.

Contact person: Anna Marie Bohmann

Abstract: TBA

Contact person: Chris Kapulkin