Complex Geometry Seminar
Student No.:20
Time:Fri 15:20-16:20, Oct.12-Dec.14
Instructor:Akito Futaki  [Tsinghua University]
Place:Conference Room 1, Jin Chun Yuan West Bldg.
Starting Date:2018-10-12
Ending Date:2018-12-14


Speaker: Yashan Zhang (BICMR, Peking University)

Title: Infinite-time singularity type of the Kaehler-Ricci flow

In this talk, we shall discuss some classification results on infinite-time singularity type of the Kaehler-Ricci flow on compact minimal Kaehler manifolds, focusing on their relation to the underlying complex structures. In particular, we shall provide a new criterion for type IIb singularities when the manifold is of Kodaira dimension one.


Speaker: Jun Li (Hunan University)

Title: Geometrical pluripotential theory on Sasaki manifolds

In this presentation I will talk about the geometric structures on the space of transverse Kahler potentials in Sasaki setting.
These results will be used to solve the problem about the existence of Sasaki metrics with constant scalar curvature in terms of properness of K-energy.
This is a joint work with Weiyong He.


Speaker: Chien Lin (Tsinghua University)

Title: On the CR Analogue of Three Circle Theorem

In this talk, we will give the proof of the CR analogue of three circle theorem in a complete Sasakian manifold (that is of vanishing pseudohermitian torsion), which is an odd dimensional counterpart of Kähler geometry. As its applications, we are able to obtain the CR Laplacian comparison theorem and the sharp dimension estimate immediately.


Speaker: Xiaokui Yang (Chinese Academy of Sciences)

Title: RC-positivity and scalar-flat metrics on ruled surfaces

In this presentation we shall discuss the existence of scalar-flat Hermitian metrics on compact complex manifolds. This is a joint work with Jun Wang.


The time and place are different from ordinary Complex Geometry Seminar.

Time: October 17th (Wednesday), 17:05-18:05

Place: Lecture Hall, Jin Chun Yuan West Bldg.

Speaker: Kaoru Ono (Kyoto University)

Title: Some criteria for (super) heavy subsets in symplectic manifolds

(Super) heavy subsets are, in some sense, Floer theoretically non-trival subsets.
The notion is due to Entov and Polterovich, who showed interesting results.
After explaining basics of their theory, I would like to discuss some criteria for (super) heavy subsets.


Speaker: Feng Wang (Zhejiang University)

Title: The existence of Kahler-Einstein metrics on K-polystable Q-Fano varieties with non-positive discrepancies

I will talk out the recent work with Gang Tian and Chi Li. At first, we extend Tian’s solution of Yau-Tian-Donaldson conjecture to the log smooth case. Then for a K-polystable Q-Fano varieties X with non-positive discrepancies, we show that there exists conic KE metrics on the resolution and these metrics converges to the singular KE metric on X.