Conference on Special Metrics in Complex Geometry

复杂几何特殊度量会议

• 批准号: 1841018
• 负责人: Ronan Conlon
• 金额: $ 2.15万
• 依托单位: Florida International University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-03-01 至 2021-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1841018&HistoricalAwards=false
• 关键词: Conference; Special; Metrics; Complex; Geometry

The Conference on Special Metrics in Complex Geometry will be held at Florida International University from January 7-10, 2021. Complex manifolds are higher-dimensional surfaces that are defined using the complex numbers. Recently, there has been significant progress in the study of "metrics" on complex manifolds, objects that endow these spaces with a shape or more precisely, curvature. The study of these metrics lies at the nexus of complex geometry and geometric analysis. The aim of this conference is to gather together experts working in these two fields to discuss these new and exciting developments. Even though lately there have been many conferences in complex geometry, none have really been organised to address these recent discoveries. This conference serves to fulfill this necessity. In doing so, it will promote collaboration across many areas of the aforementioned fields of complex geometry and geometric analysis. The latest breakthroughs in these two fields will be presented to a new generation of mathematicians, with a particular emphasis on women and those from minority groups. The conference will provide a forum for senior mathematicians to interact with graduate students through the organisation of an optional poster presentation for graduate students which will take place in a non-intimidating and relaxed environment. Ample opportunity will also be provided to women speakers to present their research, with at least one talk per day scheduled for a female speaker. Moreover, the conference will provide a platform for postdocs and junior researchers to present their work. Participants will be brought up-to-date with all of the current developments in the field and will be presented with new avenues of research in the enticing environment that Miami provides in the Winter. More specifically, the Conference on Special Metrics in Complex Geometry will concentrate on the interplay between complex geometry and geometric analysis, with an emphasis being given to equations arising in the construction of hermitian and Kahler metrics with prescribed curvature properties, for example, the complex Monge-Ampere equation in Kahler geometry. These equations are among the most important appearing in geometric analysis and understanding their structure and the techniques involved in their solution are paramount for further progress in the field. Recent breakthroughs include, among others, the independent construction of non-flat Ricci-flat Kahler metrics with maximal volume growth on complex affine space of dimensions three and greater by Li, Conlon-Rochon, and Szekelyhidi, the construction of new examples of gradient expanding and steady Kahler-Ricci solitons by Conlon-Deruelle and Biquard-Macbeth respectively, the solution by Chen-Cheng of a major conjecture of Tian stating the equivalence between the existence of constant scalar curvature Kahler metrics on a compact Kahler manifold and the properness of Mabuchi's K-energy, and the recent families of Ricci-flat Kahler metrics exhibited by Hein-Sun-Viaclovsky-Zhang on K3 surfaces which collapse to an interval with Tian-Yau and Taub-NUT metrics occurring as bubbles. These topics will all form part of the conversation at the conference in January 2021. More details will be available at http://faculty.fiu.edu/~rconlon/conference.htmThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

复几何中的特殊计算会议将于2021年1月7日至10日在佛罗里达国际大学举行。复流形是使用复数定义的高维曲面。最近，在复流形上的“度量”研究方面取得了重大进展，这些物体赋予这些空间形状或更准确地说，曲率。这些度量的研究是复几何与几何分析的结合点。本次会议的目的是聚集在这两个领域的专家，讨论这些新的和令人兴奋的发展。尽管最近有许多会议在复杂的几何，没有真正组织解决这些最近的发现。这次会议就是为了满足这一需要。在这样做时，它将促进上述复杂几何和几何分析领域的许多领域的合作。这两个领域的最新突破将呈现给新一代的数学家，特别强调女性和少数群体。会议将为高级数学家提供一个论坛，通过为研究生组织一个可选的海报演示，与研究生互动，这将在一个非恐吓和轻松的环境中进行。还将为女发言者提供充分的机会介绍她们的研究，每天至少安排一名女发言者发言。此外，会议将为博士后和初级研究人员提供一个展示他们工作的平台。参与者将了解该领域的所有最新发展，并将在迈阿密冬季提供的诱人环境中了解新的研究途径。更具体地说，在复杂的几何特殊的计算会议将集中在复杂的几何和几何分析之间的相互作用，重点是给予在建设厄米特和卡勒度量与规定的曲率属性，例如，卡勒几何复杂的蒙格-安培方程所产生的方程。这些方程是几何分析中出现的最重要的方程之一，理解它们的结构和解决它们的方法对于该领域的进一步发展至关重要。最近的突破包括Li，Conlon-Rochon和Szekelyhidi在三维及更高维的复仿射空间上独立构造了具有最大体积增长的非平坦Ricci平坦Kahler度量，Conlon-Deruelle和Biquard-Macbeth分别构造了梯度扩展和稳定的Kahler-Ricci孤子的新例子，Chen-Cheng解决了Tian的一个主要猜想，该猜想说明了紧致Kahler流形上常数量曲率Kahler度量的存在性与Mabuchi K-能量的适当性之间的等价性，最近Hein-Sun-Viaclovsky-Zhang在K3曲面上展示的Ricci-平坦Kahler度量族，它们坍缩到一个区间，Tian-Yau和Taub-NUT度量以气泡形式出现。这些主题都将成为2021年1月会议对话的一部分。 更多细节将在www.example.com上提供http://faculty.fiu.edu/~rconlon/conference.htmThis奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。