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

关于复分析、微分几何和偏微分方程的会议这是一个为期一周的会议，围绕着几何中的正则度量这一主题，讨论了复分析、微分几何和偏微分方程式的许多方面。特别重要的是最近的发展，如乘子理想层、Bergman核和几何不变理论中的渐近稳定性、哈密顿动力学和复Monge-Ampere方程、几何热流和能量泛函。正则度规通常涉及非线性偏微分方程组，其中未知量是张量。它们起源于几何和拓扑学，但它们也与理论物理中的基本方程密切相关，如杨-米尔斯方程和广义相对论中的爱因斯坦方程。这些问题通常很难解决，但最近从许多不同的方向涌入了许多新想法。这次会议将有助于顶尖专家之间的思想交流，并向新一代年轻学生和博士后研究人员介绍该领域的问题和方法。

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.