IMSA Distinguished Lecture Series: Geometry in the South

Professor Anna Maria Fino, FIU and University of Torino: Non-Kahler manifolds via mapping tori 

In the talk I will report some results on existence of special Hermitian structures, like balanced, CYT and SKT on mapping tori. In the first part of the talk I will show a construction via toric suspensions of hyperKa-hler manifolds, obtained in collaboration with Gueo Grantcharov and Misha Verbitsky. Next, I will discuss joint results with Beatrice Brienza and Gueo Grantcharov on compact complex manifolds admitting a Hermitian structure which is SKT and CYT, but not Bismut flat.

Professor Xiuxiong Chen, Stony Brook and Hefei: On the constant Scalar Curvature Kaehler metrics

Inspired by the famous a priori estimate due to Calabi, Yau on K\"ahler Einstein metrics, we establish an apriori estimate for constant scalar curvature Kaehler metrics. This is a joint work with J. R. Cheng.