Conference on Complex Analysis, Differential Geometry, and Partial Differential Equations; May 2-6, 2005; New York, NY

复分析、微分几何和偏微分方程会议；

• 批准号: 0456822
• 负责人: Duong Phong
• 金额: $ 3万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-04-01 至 2006-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0456822&HistoricalAwards=false
• 关键词: Conference; Complex; Analysis; Differential; Geometry

Conference on Complex Analysis, Differential Geometry, and Partial Differential EquationsThis is a week-long conference on the many aspects ofcomplex analysis, differential geometry, and partialdifferential equations centered around the theme ofcanonical metrics in geometry. Of particular importanceare recent developments such as multiplier ideal sheaves,Bergman kernels and asymptotic stability in geometricinvariant theory, Hamiltonian dynamics and complex Monge-Ampereequations, geometric heat flows, and energy functionals.Canonical metrics involve typically a non-linear systemof partial differential equations, where the unknown is atensor. They arise from geometry and topology, but theyare also closely to basic equations from theoreticalphysics such as Yang-Mills equations and Einstein'sequations in general relativity. They are usually verydifficult to solve, but there has been recently an influxof new ideas from many different directions. This conferencewill help cross-fertilization of ideas between the leadingexperts, and introduce a new generation of young studentsand postdoctoral researchers to problems and methods in thearea.

复分析、微分几何和偏微分方程会议这是一个为期一周的会议，讨论复分析、微分几何和偏微分方程的许多方面，会议的主题是几何中的规范度量。特别重要的是最近的发展，如乘子理想轴，伯格曼核和几何不变理论中的渐近稳定性，哈密顿动力学和复杂蒙日-安培方程，几何热流和能量泛函。典型度量通常涉及一个非线性偏微分方程组，其中未知量是张量。它们起源于几何学和拓扑学，但它们也接近于理论物理学中的基本方程，如广义相对论中的杨-米尔斯方程和爱因斯坦方程。这些问题通常很难解决，但最近有许多来自不同方向的新想法涌入。本次会议将有助于专家之间的思想交流，并向新一代青年学生和博士后研究人员介绍该领域的问题和方法。