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

一个名为《广义相对论九十九年》的暑期班将于2014年7月28日至8月1日在奥地利维也纳的欧文·薛定谔研究所举办。这个暑期班将考察几何分析(微分几何、偏微分方程式)的主题，这些主题目前对数学广义相对论很感兴趣。爱因斯坦方程在广义相对论和黎曼几何中具有基本的重要性，而爱因斯坦方程作为引力现象的模型的研究涉及几何分析和物理之间的深层关系。近年来在几个方面取得了令人瞩目的进展，包括研究黑洞时空上的波动方程(最终目标是了解黑洞的稳定性)、宇宙审查、真空中黑洞的动态形成、黑洞的拓扑以及对爱因斯坦约束方程解的模空间的更好理解，爱因斯坦约束方程支配柯西问题的初始数据的几何。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(在构建约束的解决方案和理解这些初始数据集的演变方面)，并在这些领域的研究人员之间建立桥梁。暑期班的目的是向研究生和博士后介绍接近这些结果所需的背景知识，并介绍该领域一些突出的公开问题。该计划将由四个迷你课程组成，并辅之以几个小时的入门和专题讲座。在暑期学校的网页上可以看到详细信息：http://homepage.univie.ac.at/piotr.chrusciel/SummerSchool2014/index.htmlThere在世界各地都存在，一个充满活力的数学家和物理学家社区，他们在数学相对论方面取得了进展。天体物理观测和对引力波的搜索继续给研究人员带来理论和实验上的挑战。《广义相对论九十九年》暑期班将向研究生和博士后介绍解决这些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、欧洲和其他地方的知名研究人员、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，尤其是要把兴趣从理论到应用，从几何分析到天体物理和数值分析的学生和研究人员聚集在一起。这笔赠款将为15名美国研究生和博士后提供资金，让他们参加暑期班。

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.