Program:

 

April 20:

8:55: Opening Remarks

9:00-9:45: Wang Zuoqin

9:55-10:40: Huang Yong

11:00-11:45: Han Qing, Mini-Lectures 1

 

14:00-14:45: Sheng Li

14:55-15:40: Wang Kelei

16:00-16:45: Sun Wei

 

April 21:

9:00-9:45: Xia Chao

9:55-10:40: Han Xiaoli

11:00-11:45: Han Qing, Mini-Lectures 2

 

14:00-14:45 Wang Fang

14:55-15:40 Jiao Heming

16:00-16:45 Chen Chuanqiang

 

Abstracts:

 

Speaker: Chen Chuanqiang (Zhejiang University of Technology)

Title: Some estimates of Hessian quotient equations

Abstract: In this talk, we introduce the interior gradient estimates and global $C^2$ estimates of Neumann problems of Hessian quotient equations.

 

Speaker: Han Xiaoli (Tsinghua University)

Title: The new way to find the holomorphic curve and the special Lagrangian surfaces

Abstract: I will introduce one new way to find the holomorphic curves and special Lagrangian surfaces in Kahler-Einstein surfaces using the new functional.

 

Speaker: Huang Yong (Hunan University)

Minkowski Problems of Convex Bodies

Title: In this talk, I will report briefly on the development of Minkowski problems of convex bodies during the past 120 years. The variational and continuity methods to solve those problems will be discussed. In particular, I will also discuss a recent joint work with Erwin Lutwak, Deane Yang and Gaoyong Zhang. 

 

Speaker: Jiao Heming (HIT)

Title: Second order estimates for Hessian type elliptic equations on Riemannian manifolds.

Abstract: I will report some joint works with Bo Guan about the a priori estimates for general Hessian type equations on Riemannian manifolds. In these works we are able to derive the estimates under a "minimal" set of assumptions which are standard in the literature. These estimates enable one to prove some existence results.

 

Speaker: Sheng Li

Title: Homogeneous toric bundles and generalized Abreu equations

Abstract: We study the generalized Abreu equation on a Delzant ploytope. We can generalize the result of Chen-Han-Li-S. to homogeneous toric bundles. We talk some differential inequalities and some estimates for homogeneous toric bundles, and the existence of the constant scalar metrics of homogeneous toric bundles under the assumption of an appropriate stability. The works are joint with Chen bohui, Han Qing, Li An-Min and Lian Zhao.

 

Speaker: Sun Wei (Fudan University)

Title: Parabolic complex Monge–Amp\`re type equations on closed manifolds
Abstract: The complex Monge-Amp\`ere type equations include some of the most important differential equations in complex geometry. Besides the continuity method, the parabolic flow method is also very effective. In this talk, I will report my work on parabolic complex Monge-Amp\`ere type equations under the cone condition.

 

Speaker: Xia Chao (Xiamen University)

Title: Inverse anisotropic mean curvature flow and Minkowski inequality

Abstract: In this talk, I will talk about the inverse anisotropic mean curvature flow from a star-shaped hypersurface and show such flow exists for long time and converges to a rescaled Wulff shape.  As an application, we prove the Minkowskis inequality for mixed volumes. If time permits, I will discuss general inverse anisotropic curvature flows from convex hypersurfaces.

 

Speaker: Wang Fang (Shanghai Jiaotong University)

Title: On the positivity of scattering operators for Poincar\’e-Einstein manifolds

Abstract: On Poincar\’e-Einstein manifolds the scattering operators, associated to the interior scalar Laplacian, define a meromorphic family of conformally covariant pseudo-differential operators. Here I will mainly talk about the relationship between the positivity of the scattering operators and the positivity of the conformal geometry at the boundary. 

 

Speaker: Wang Kelei (Wuhan University)

Title: Regularity of flat level sets in phase transition models

Abstract: In this talk I will discuss a new proof of Savin's result on the uniform $C^{1,\alpha}$ regularity of flat level sets in the Allen-Cahn equation and its application to De Giorgi conjecture, as well as a uniform $C^{2,\alpha}$ regularity of flat level sets in a phase transition model with free boundary and its application to the classification of finite Morse index solutions in the plane.

 

Speaker: Wang Zuoqin (USTC)

Title: Recovering the Schrodinger potentials on toric manifolds 

Abstract: Let $P$ be a semi-classical Schrodinger operator on some Riemannian manifold. We are interested in the relation between its spectrum and the potential function of $P$. In this talk I will explain the conception of the equivariant spectrum in the case that the manifold  admits some symmetry, and will introduce our work (joint with Prof. Victor Guillemin) on recovering the Schrodinger potentials on symplectic toric manifolds.