Great Lakes Geometry Conference

五大湖几何会议

• 批准号: 0302452
• 负责人: Xiuxiong Chen
• 金额: $ 1.5万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-04-15 至 2004-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0302452&HistoricalAwards=false
• 关键词: Great; Lakes; Geometry; Conference

AbstractAward: DMS-0302452Principal Investigator: Xiu Xiong ChenThe next Great Lakes Geometry Conference will be held May 1 - 4,2003 at the University of Wisconsin-Madison. This is aninternational conference held annually in the Midwest region,rotating among different universities. The aim of this conferencewill be to introduce the latest developments in the field ofgeometric analysis and some closely related areas. A partiallist of topics which will be covered by this conference include:(Kaehler-) Einstein equation and constant scalar curvature metricequation (Yamabe problem); (Hermitian-) Yang-Mills equation;minimal surface equation; harmonic map problem and J- holomorphiccurves (Cauchy-Riemann equation); and the geodesic equation inthe infinite dimensional space of Kaehler metrics which is givenby a homogenous complex Monge-Ampere equation. These equationsfit together with the corresponding evolution equations:(Kaehler-) Ricci flow, Yang-Mills flow, the mean curvature flow,and the harmonic map flow, etc. People would like to know (localand global) existence, regularity and uniqueness of solutions tothese equations. Many deep works have arisen by studyingdifferent aspects of these challenging problems.Differential geometry is a fundamental and vital field ofmathematics which has many far reaching applications beyond therealm of pure mathematics. To name a few: the study of Kaehlergeometry, especially Calabi-Yau manifolds, has importantapplications in theoretical physics; the study of (inverse) meancurvature flow has important applications in image processing;and the study of curves, surfaces and their higher-dimensionalanalogues have important applications in computer graphics,engineering and optimization.

摘要奖项：DMS-0302452首席研究员：陈秀雄下届五大湖几何会议将于2003年5月1日至4日在威斯康星大学麦迪逊分校举行。这是每年在中西部地区举行的国际会议，在不同大学之间轮流举行。本次会议的目的是介绍几何分析领域和一些密切相关领域的最新进展。 本次会议将涵盖的部分主题包括：（Kaehler-）爱因斯坦方程和常标量曲率度量方程（Yamabe问题）； (Hermitian-) Yang-Mills 方程；最小曲面方程；调和映射问题和J-全纯曲线（柯西-黎曼方程）；以及由齐次复Monge-Ampere方程给出的Kaehler度量无限维空间中的测地方程。 这些方程与相应的演化方程拟合在一起：(Kaehler-)Ricci流、Yang-Mills流、平均曲率流、调和映射流等。人们想知道这些方程解的(局部和全局)存在性、规律性和唯一性。 通过研究这些具有挑战性的问题的不同方面，出现了许多深入的工作。微分几何是数学的一个基础和重要领域，它在纯数学领域之外具有许多深远的应用。仅举几例：Kaehl几何学，特别是Calabi-Yau流形的研究，在理论物理中有重要的应用； （逆）平均曲率流的研究在图像处理中具有重要的应用；曲线、曲面及其高维类似物的研究在计算机图形学、工程和优化中具有重要的应用。