IHP: Program in Conformal and Kahler Geometry

这笔赠款将支持2012年秋季在法国巴黎的亨利·庞加莱研究所开展的一个共形几何和卡勒几何主题的项目。 这三个月将开始两个介绍性的迷你课程，随后为期一周的会议共形和卡勒几何（9月17日至21日），这将涵盖该计划的广泛的数学主题：共形不变量，庞加莱-爱因斯坦度量，自对偶性，共形几何中的非线性偏微分方程，临界卡勒度量和复杂的蒙格-安培方程。 这三个月的其他活动将试图详细阐述介绍性会议中的有关发展，并使其更加突出重点。 本学期晚些时候将有三个更小，更集中的研讨会：几何和物理（10月8日至12日），几何PDE（11月5日至9日）和Kahler几何的最新发展（12月10日至14日）。 同时还将举办一系列专题小型课程。 共形几何起源于世纪对复变函数的研究。 粗略地说，它是对空间变换的研究，它可能会扭曲距离的测量，但不是如何测量角度。 保形映射在许多应用科学中起着基础作用，现代保形几何与理论物理和材料科学有着密切的联系。 卡勒几何是复几何的一个分支，它与物理学和现代几何的许多领域都有着重要的联系。该计划的目标是提供该领域在这些领域的现状概述，促进研究人员之间的互动，并教育研究生和博士后学者对开放问题和最新技术。

This grant will support a program in the Fall of 2012 at the Institut Henri Poincare in Paris, France, on the theme of Conformal and Kahler geometry. The trimester will begin with two introductory mini-courses followed by the week-long conference Conformal and Kahler Geometry (September 17-21), which will cover the broad mathematical themes of the program: conformal invariants, Poincaré-Einstein metrics, self-duality, nonlinear PDEs in conformal geometry, critical Kahler metrics, and complex Monge-Ampere equations. The other activities throughout the trimester will attempt to elaborate and bring into sharper focus the developments related in the introductory conference. There will be three smaller and more focused workshops later in the term: Geometry and Physics (October 8-12), Geometric PDE (November 5-9), and Recent Developments in Kahler Geometry (December 10-14). These will be accompanied by a series of topical mini-courses. Conformal geometry has its origins in the study of functions of a complex variable in the nineteenth century. Roughly speaking, it is the study of transformations of a space which may distort the measurement of distances, but not how one measures angles. Conformal mappings play a basic role in many applied sciences, and modern conformal geometry has connections to theoretical physics and materials science. Kahler geometry is a branch of complex geometry which also has important ties to physics and many areas of modern geometry. The goals of this program are to provide an overview of the current state of the field in these areas, foster interactions between researchers and educate graduate students and postdoctoral scholars on open problems and recent techniques.