##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Hassan Jolany

#### UCSD

## Classification of Kahler varieties via Song-Tian program

##### Abstract:

Mori introduced a program for classifying projective varieties by using algebraic surgeries, Jian Song and Gang Tian introduced Analytical Minimal Model Program for the classification of Kahler varieties by using PDE surgeries. For the intermediate Kodaira dimension they proved that there exists a unique generalized Kahler-Einstein metric which twisted with Weil-Petersson metric. I extended their result in my PhD thesis on pair $(X,D)$ where $D$ is a snc divisor with conic singularities and I showed that there exists a generalized Kahler-Einstein metric which twisted with logarithmic Weil-Petersson metric plus additional term which we can find such additional term by using higher canonical bundle formula of Fujino and Mori. Moreover I extended Song-Tian program for Sasakian varieties in my PhD thesis. In fact when the basic first Chern class of a Sasakian variety is not definite then the question is how can we find generalized Kahler-Einstein metric for such varieties. I gave a positive answer to this question in my thesis. Moreover I will explain how the Lei Ni method which later improved by V.Tosatti for the classification of the solution of Kahler-Ricci flow could be extended to conical Kahler-Ricci flow and I finally will explain how the classification of the solutions of relative Kahler-Ricci flow is related to the Gromov invariant of Ruan-Tian.

Organizer: Lei Ni

### October 12, 2016

### 3:00 PM

### AP&M 7321

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