Constant Scalar Curvature Metrics in Sasaki and Kahler Geometry

该奖项支持美国研究人员参加将于2018年1月15日至2018年1月19日在法国CIRM举行的为期一周的纯数学国际会议。会议的题目是“Sasaki和Kahler几何中的常数标量曲率”。“是次会议旨在介绍及进一步发展复杂几何中最基本的猜想之一--姚田-唐纳森猜想的最新成果。 该猜想是在两个不同的领域，有深刻的影响，在纯数学和现代物理学的交叉点：微分几何和代数几何。 这次会议的目的，是召集国际上一些在Y-T-D猜想的几个方面的专家，让他们相互交流，并与有新鲜想法的年轻研究人员进行互动，以便在解决最普遍的猜想方面取得进展。这次会议将作为一个学习的机会，以及一种方式，以帮助建立联系，开辟数学合作的道路。与会者将来自不同的背景和国家，组委会将促进数学科学代表性不足的群体的出席。自从2012年Yau-Tian-唐纳森关于Kahler-Einstein度量的存在性与K-多稳性等价的猜想被证明以来，Kahler几何学家们开始将这一猜想推广到常数量曲率（csc）Kahler/Sasaki度量的存在性.这个扩展远不是一个微不足道的问题，因为csc方程是更困难的（非线性四阶偏微分方程）。尽管如此，这一课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。 会议的主题在于以下研究领域的十字路口：复杂/CR几何，辛/接触几何，复杂的代数几何，几何不变理论和代数稳定性，模空间，复分析，几何量化，热核渐近，几何流和偏微分方程，数学物理。因此，人们可以希望，技术的发展和揭示的关系将产生影响的其他领域的几何，作为研究爱因斯坦度量，特殊holonomy几何，模空间的卡勒度量和模的代数簇，仅举几例。上述各个子领域之间的相互作用在过去一直是富有成果的，人们自然希望这些子领域中的一些可以从Yau-Tian-唐纳森猜想的进展中受益。会议的网站位于：http://scientific-events.weebly.com/1750.html

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