2013年夏季数学科学研究中心几何学研讨会

2013-08-26 来源:数学科学研究中心

活动地点:

活动类型:学术会议

主讲人:

活动时间:

活动内容:

2013年夏季数学科学研究中心几何学研讨会

 

时间:2013年8月29日 

地点:数学中心202室

 

09:30 开幕式

 

09:40-10:40  Speaker: 刘克峰 教授

Title: Hodge metric completion of Teichmuller spaces of Calabi-Yau manifolds

 

Abstract:I will discuss our proof of the existence of holomorphic affine structure on the Teichmuller spaces of polarized and marked Calabi-Yau manifolds and their Hodge metric completions. As corollaries we show that the extended period map from the completion space is injective into the period domain, and that the completion space is a domain of holomorphy and admits a complete Kahler–Einstein metric.

 

10:40 -11:00  茶歇

 

11:00 -12:00  Speaker: 赵恩涛 博士

Title: Some recent results on mean curvature flow of arbitrary codimensions 

 

Abstract:In this talk, I will discuss some of our recent results on the extension and convergence of mean curvature flow of submanifolds with arbitrary codimensions. The initial submanifold is assumed to satisfy suitable curvature pinching condition. The talk is based on my joint works with Prof. Kefeng Liu, Prof. Hongwei Xu and Dr. Fei Ye.

 

 

中午:工作餐

 

13:30-14:30  Speaker: 饶胜 博士 

Title: Several applications of an iteration method in deformation theory


Abstract: In this talk, I will introduce my recent joint works on deformation theory. Based on a new iteration method in Kodaira-Spencer-Kuranishi deformation theory, we derive several new global results on deformation theory, such as the global convergence of the Beltrami differentials on CY manifolds. Also based on this method, we revisit the local and global Torelli theorems for Riemann surfaces by a new differential geometric method and calculate the second fundamental form of the Torelli space's nonhyperelliptic locus, as applications of deformation formula of holomorphic one-forms to moduli problems of Riemann surfaces.

 

14:30-15:30  Speaker: 胡正宇 博士 

Title: Polarized pairs and minimal models

 

Abstract: This is a joint work with Caucher Birkar. We introduce the notion of polaried pairs and proved some basic properties. As an application, I will discuss the relation between minimal models and Zariski decompositions. I will also discuss some further applications.

 

15:30-15:50  茶歇

 

15:50-16:50 Speaker: 韦康

Title: Some topics in deformation theory on compact generalized Calabi-Yau Manifolds

 

Abstract:In this paper, we prove the deformations of a compact H-twisted generalized Calabi-Yau manifold are unobstructed in a fixed neighbourhood. And we also construct the global canonical family of the deformations.