学术报告:2019年4月30日10:00,张雅⼭,北京⼤学

发布者:吕小俊发布时间:2019-04-26浏览次数:163

东南大学数学学院邀请专家申请表

  

报告人

张雅

单位

北京北京国际数学研究中

报告题目

Generalized Kaehler-Einstein metrics and   infinite-time singularity type of the Kaehler-Ricci flow

报告时间

430日(周二)上午10

地点

四牌楼校区逸夫建筑馆1511

报告摘要

Abstract:   Recent years have seen important progresses on geometric analysis aspect of   semi-ample canonical line bundles. In this talk, we shall first recall   Song-Tian's (possibly singular) generalized Kaehler-Einstein metrics on   semi-ample canonical line bundles, and then we determine their metric   asymptotics near singular points in Kodaira dimension one case, in its   setting implying a conjecture of Song-Tian that the metric completion of the   generalized Kaehler-Einstein metric is homeomorphic to the canonical model.   Then we shall move to infinite-time singularity type (i.e. long-time Riemann   curvature behaviors) of the Kaehler-Ricci flow (KRF) on compact Kaehler   manifolds with semi-ample canonical line bundle and explain that these   results provide an analytic viewpoint to classify the complex structures on   the underlying manifolds. Finally, a precise relation between the singularity   type of KRF and certain algebro-geometric properties of the singular fibers   of the semi-ample fibration will be presented, which is a criterion for KRF   developing type IIb singularities and may be seen as an evidence for the   aforementioned classification viewpoint. Part of this talk is based on joint   works with Frederick Fong.

报告人简介

张雅山,北京大学北京国际数学研究中心博士后,研究方向是复几何与几何分析,部分成果发表在Math.Ann, IMRN, JGA, MRL, AGAG等杂志。