# List All Events

Topology/Geometry Seminar

## Kaehler-Ricci flow on Fano horosymmetric manifolds

#### Xiaohua Zhu (Peking University)

Location:  Hill Center, Room 705
Date & time: Tuesday, 24 January 2023 at 4:00PM - 5:00PM

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 constructed by a $$C^*$$-degeneration induced by an element in the Cartan torus Lie algebra of G. A similar result can be also proved for Kaehler-Ricci flows on any Fano horosymmetric manifolds.