Speaker: Yanyan Li
Time:9:00-10:00
Title: MONGE-AMPERE EQUATION WITH BOUNDED PERIODIC DATA
Abstract. We consider the Monge-Amp`ere equation det(D2u) = f in Rn, where f is a positive bounded periodic function. We prove that u must be the sum of a quadratic polynomial and a periodic function. For f ≡ 1, this is the classic result by Jorgens, Calabi and Pogorelov.For f ∈ Cα, this was proved in joint work with by Caffarelli.The work presented is a joint work with Siyuan Lu.

 

Speaker: Jianchun Chu
Time:10:10-11:10

Title: C^{1,1} regularity of geodesics of singular Kahler metrics.

Abstract：In this talk, I will first describe a joint work with Valentino Tosatti and Ben Weinkove on optimal C^{1,1} regularity of geodesics of Kahler metrics. Next, I will show the optimal C^{1,1} regularity of geodesics of Kahler metrics on compact Kahler varieties away from the singular locus. This is a joint work with Nicholas McCleerey. A key step is to establish the boundary estimate for the complex Monge-Ampere equation that does not require strict positivity of the reference form near the boundary.

 

Speaker：Jingyi Chen
Time:14:00-15:00
Title：Some recent development on Hamiltonian stationary Lagrangian submanifolds
Abstract: We will discuss some recent results on regularity, removable singularity and convergence 
of Hamiltonian stationary Lagrangian submanifolds in C^n. This is based on joint work with M. Warren.

 

Speaker: Feng Wang
Time:15:30-16:30

Title: YTD conjecture for uniform K-stable Q-Fano varieties
Abstract: I will talk about the existence of weak KE metrics on uniform stable Q-Fano varieties by adapting BBJ's method. 

 

Speaker: Chi Li
Time:16:40-17:40

Title: On the equivariant uniform stability and Yau-Tian-Donaldson conjecture
Abstract: I will prove that if a singular $Q$-Fano variety $X$ is $Aut^0(X)$-uniformly K-stable, then it admits a Kahler-Einstein metric. This generalizes the our previous work on uniform version of Yau-Tian-Donaldson conjecture for singular Fano varieties. A key new ingredient is a valuative criterion for G-uniform stability for any $Q$-Fano variety.