Ninety-Nine Years of General Relativity: ESI-EMS-IAMP Summer School on Global Aspects of Mathematical Relativity

2014年7月28日至8月1日，一个名为“广义相对论99年”的暑期学校将在Erwin Schrödinger研究所（奥地利维也纳）举行。本暑期学校将研究当前对数学广义相对论感兴趣的几何分析（微分几何，偏微分方程）主题。爱因斯坦方程在广义相对论和黎曼几何中具有重要的基础意义，将爱因斯坦方程作为引力现象的模型进行研究涉及几何分析和物理之间的深刻关系。近年来在几个方面取得了惊人的进展，包括黑洞时空波动方程的研究（最终目标是理解黑洞的稳定性），宇宙审查，真空中黑洞的动力学形成，黑洞的拓扑结构，以及对控制柯西问题初始数据几何的爱因斯坦约束方程解的模空间的更好理解。引力现象数值分析的最新进展突出表明，需要突破初值公式的理论界限（包括构造约束的解和理解这些初始数据集的演变），并在这些领域的研究人员之间建立一座桥梁。暑期学校的目的是向研究生和博士后介绍研究这些结果所需的背景知识，并提出该领域一些突出的开放性问题。该计划将包括四个迷你课程，辅以几个小时的入门和专题讲座。在暑期学校的网页上可以找到详细信息：http://homepage.univie.ac.at/piotr.chrusciel/SummerSchool2014/index.htmlThere在世界各地有一个充满活力的数学家和物理学家社区，他们正在数学相对论方面取得进展。天体物理观测和对引力波的探索继续为研究人员提供理论和实验上的挑战。暑期课程《广义相对论九十九年》将向研究生和博士后介绍解决这些问题和该领域其他突出问题所需的工具。该学院还将促进来自美国、欧洲和其他地区的知名研究人员、研究生和博士后之间的互动。招募和支持该领域的年轻人才至关重要，特别是将学生和研究人员聚集在一起，他们的兴趣跨越理论到应用，从几何分析到天体物理学和数值分析。这笔拨款将为15名美国研究生和博士后提供参加暑期学校的资金。

A summer school, Ninety-Nine Years of General Relativity, will be held at the Erwin Schrödinger Institute (Vienna, Austria), July 28-August 1, 2014. This summer school will examine topics in geometric analysis (differential geometry, partial differential equations) of current interest in mathematical general relativity. The Einstein equation is of fundamental importance in general relativity and Riemannian geometry, and the study of the Einstein equation as a model for gravitational phenomena involves deep relationships between geometric analysis and physics. Spectacular progress has been made in recent years on several fronts, including the study of wave equations on black hole space-times (with the eventual goal of understanding black hole stability), cosmic censorship, dynamical formation of black holes in vacuum, topology of black holes, and a better understanding of the moduli space of solutions to the Einstein constraint equations which govern geometry of initial data for the Cauchy problem. Recent advances in numerical analysis of gravitational phenomena highlight the need to push the theoretical boundaries of the initial value formulation (both in constructing solutions to the constraints and in understanding the evolution of these initial data sets) and to create a bridge between the researchers in these areas. The purpose of the summer school is to introduce graduate students and postdocs to the background needed to approach these results and to frame some outstanding open problems in the field. The program will consist of four mini-courses supplemented by several hours of lectures on both introductory and special topics. Details are available at the summer school webpage: http://homepage.univie.ac.at/piotr.chrusciel/SummerSchool2014/index.htmlThere exists around the world a vibrant community of mathematicians and physicists who are making progress on mathematical relativity. Astrophysical observations and the search for gravitational waves continue to provide researchers with both theoretical and experimental challenges. The summer school Ninety-Nine Years of General Relativity will introduce graduate students and postdocs to the tools needed to approach these and other outstanding problems in the field. The school will also foster interaction amongst established researchers, graduate students and postdocs, from the U.S., Europe and elsewhere. It is of crucial importance to recruit and support young talent in the field and, in particular, to bring together students and researchers whose interests span the theoretical to the applied, from geometric analysis to astrophysics and numerical analysis. The grant will provide funding for fifteen U.S. graduate students and postdocs to attend the summer school.