##### Department of Mathematics,

University of California San Diego

****************************

### Math 258: Seminar in Differential Geometry

## Xiaohua Zhu

#### Peking U

## Kaehler-Ricci flow on Fano G-manifolds

##### Abstract:

I will talk about a recent work jointly with Tian on Kaehler-Ricci flow on Fano G-manifolds. We prove that on a Fano G-manifold, the Gromov-Hausdorff limit of Kaehler-Ricci flow with initial metric in $2\pi c_1(M)$ must be a Q-Fano horosymmetric variety which admits a singular Keahler-Ricci soliton. Moreover, we show that the complex structure of limit variety can be induced by $C^*$-degeneration via the soliton vector field. A similar result can be also proved for Kaehler-Ricci flows on any Fano horosymmetric manifolds.

Host: Lei Ni

### October 20, 2022

### 4:00 PM

Zoom ID: 953 0943 3365

****************************