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Title：Kähler-Einstein metrics and volume comparison in Kähler geometry

Speaker：张科伟  博士 (北京师范大学)

时间：2022年1月2日（星期天）上午9:00-11:00

地点：腾讯在线会议   会议 ID：808 9159 5567

Abstract

 I will talk about some recent progress on the study of the Yau-Tian-Donaldson conjecture, whose goal is to search for canonical metrics on algebraic manifolds. The canonical metrics we will be focusing on are the "twisted Kähler Einstein metrics". The existence of such metrics can be related to the so called "delta invariant", which has gained a lot of research interest in the recent literature. We will prove some basic properties of delta invariant and as an application we show that delta invariant can be used to prove a Kählerian Bishop type theorem, which states that the volume of a compact Kähler manifold with positive Ricci curvature cannot be bigger than that of the complex projective space.

This talk will probably be divided into several parts, depending on how many details of the proof will be covered. In the first part I plan to survey some history and present the most recent results in this field, which will take about 2h. Then I will focus on the proof of Kählerian Bishop theorem, which will take 2+2 hours.

联系人:李荣刚

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