Constant Scalar Curvature Metrics in Sasaki and Kahler Geometry

Sasaki 和 Kahler 几何中的常标量曲率度量

• 批准号: 1743449
• 负责人: Hongnian Huang
• 金额: $ 1.26万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1743449&HistoricalAwards=false
• 关键词: Constant; Scalar; Curvature; Metrics; Sasaki

This award supports participation of US based researchers in a one week long international conference in pure mathematics to be held at the CIRM (France), Jan 15, 2018 - Jan 19, 2018. The title of the conference is "Constant Scalar Curvature Metrics in Sasaki and Kahler Geometry." The conference aims at presenting and further developing the latest achievements in the Yau-Tian-Donaldson conjecture, which is one of the most fundamental conjectures in complex geometry. The conjecture is at the intersection of two different domains that have deep impact in pure mathematics and modern physics: differential geometry and algebraic geometry. The goal of the meeting is to gather some of the world experts in the several aspects of the Y-T-D conjecture and have them exchange ideas among themselves as well as interact with junior researchers with fresh ideas so as to make progress in the solution of the most general version of the conjecture. The conference will serve as a learning opportunity as well as a way to help make connections and open the way to mathematical collaborations. The participants will come from diverse backgrounds and countries and the organizing committee will promote attendance of underrepresented groups in the mathematical sciences. Since the conjecture of Yau-Tian-Donaldson stating the equivalence between the existence of Kahler-Einstein and K-polystability has been proved in 2012, Kahler geometers are turning to the extension of this conjecture to existence of constant scalar curvature (csc) Kahler/Sasaki metrics. This extension is far from being a trivial question since the csc equation is by far more difficult (non-linear 4th order PDE). Nevertheless, this topic is now booming and in the last few years many related results have been proved. The determination of the organizers is to make the conference an opportunity to present and further develop the latest achievements of the subject and to promote interaction between researchers of the domain. The topics of the conference lie at the crossroads of the following research fields: complex/CR geometry, symplectic/contact geometry, complex algebraic geometry, Geometric Invariant Theory and algebraic stability, moduli spaces, complex analysis, geometric quantization, heat kernels asymptotics, geometric flows and partial differential equations, mathematical physics. Consequently, one can hope that the techniques developed and the unveiled relations will have an impact on other areas of Geometry, as the study of Einstein metrics, special holonomy geometries, moduli spaces of Kahler metrics and moduli of algebraic varieties, just to name a few. The stimulating interaction of the different sub-fields above has always been fruitful in the past and it is natural to hope that some of these sub-fields can benefit from the advances on the Yau-Tian-Donaldson conjecture in a long range.The website of the conference is located at: http://scientific-events.weebly.com/1750.html

该奖项支持美国研究人员参加为期一周的纯数学国际会议，会议将于2018年1月15日至2018年1月19日在CIRM(法国)举行。会议的题目是“佐佐木和卡勒几何中的恒定标量曲率度量”。这次会议旨在介绍和进一步发展复杂几何中最基本的猜想之一的Yau-Tian-Donaldson猜想的最新成果。这个猜想是在两个不同的领域的交集，这两个领域对纯数学和现代物理都有深远的影响：微分几何和代数几何。会议的目的是聚集世界上一些Y-T-D猜想方面的专家，让他们相互交流意见，并与具有新想法的初级研究人员互动，以便在解决最一般版本的猜想方面取得进展。这次会议将是一个学习机会，也是帮助建立联系和打开数学合作之路的一种方式。与会者将来自不同的背景和国家，组委会将促进数学科学中代表性不足的群体的出席。自从Yau-Tian-Donaldson的猜想在2012年证明了Kahler-Einstein的存在与K-多稳定性之间的等价性以来，Kahler几何学家开始将这一猜想推广到恒定标量曲率(CSC)Kahler/Sasaki度量的存在。这远不是一个微不足道的问题，因为CSC方程到目前为止要困难得多(非线性四阶偏微分方程组)。然而，这个话题现在正在蓬勃发展，在过去的几年里，许多相关的结果已经得到了证明。组织者的决心是使会议成为展示和进一步发展该学科的最新成果的机会，并促进该领域研究人员之间的互动。会议的主题位于下列研究领域的十字路口：复/CR几何、辛/接触几何、复代数几何、几何不变理论和代数稳定性、模空间、复分析、几何量子化、热核渐近、几何流动和偏微分方程、数学物理。因此，人们可以希望所开发的技术和揭示的关系将对几何学的其他领域产生影响，例如爱因斯坦度量、特殊完整几何、Kahler度量的模空间和代数簇的模，仅举几例。过去，上述不同子领域之间的激励性相互作用一直是卓有成效的，人们自然希望其中一些子领域能够长期受益于尤田-唐纳森猜想的进展。会议的网站是：http://scientific-events.weebly.com/1750.html