Special Session on Mathematical Relativity at CADS 5

爱因斯坦方程在过去的几年里取得了非凡的发展，例如黑洞形成的结果，对克尔解的唯一性和稳定性的研究，以及我们对宇宙审查，准局域质量，初始数据集变形和边缘捕获表面性质的理解的进步。 高度富有成效的连接与其他几何偏微分方程的，如杨米尔斯，波图，山边方程，各种抛物流，以及连接到其他附近地区，如谐波分析，导致了一系列令人兴奋的新发现。这项活动吸引了许多几何分析的财富的问题和潜在的应用开发的几何技术。 5月22日至26日，在以色列阿科举行的第五届复杂分析和动力系统会议上，PI组织了关于数学相对论的特别会议，旨在聚集数学相对论和几何PDE的领先专家和年轻研究人员，讨论这些问题和最新的结果，以促进合作和进一步的进展。随着几个相对论实验项目的进展，在引力物理学中，发展丰富的理论模型是非常重要的。 为了确保数学相对论继续对实验努力产生强烈的影响，并与之相互作用，这些模型应该成熟，并能够对一些主题进行定量预测，如引力坍缩，引力波和其他与强引力场相关的现象。 这次特别会议将鼓励对这些专题进行进一步的合作研究，并吸引年轻人才进入这一领域。 研究生和年轻博士的参与。这将确保学科的持续活力。

The Einstein Equations have seen extraordinary developments in the last few years, such as results on the formation of black holes, investigations into the uniqueness and stability of the Kerr solution, and advances in our understanding of cosmic censorship, quasi-local mass, deformations of initial data sets and properties of marginally trapped surfaces. Highly fruitful connections with other geometric PDE's, such as Yang Mills, wave maps, the Yamabe equation, various parabolic flows, as well as connections to other nearby areas, such as harmonic analysis, have led to an array of exciting new discoveries. This activity has attracted many geometric analysts to the wealth of problems and potential applications of the geometrical techniques developed. The special session on Mathematical Relativity organized by the PI's at the fifth conference on Complex Analysis and Dynamical Systems in Akko, Israel, May 22 to 26, aims to gather leading specialists and younger researchers in mathematical relativity and geometric PDE's, to discuss these problems and recent results in order to promote collaborations and further progress.With the advance of several experimental projects on relativistic gravitational physics, it is highly important todevelop a wealth of theoretical models. In order to assure that mathematical relativity continues to have a strong impact on, and interaction with, the experimental efforts, these models should mature and be able to make quantitative predictions on a number of subjects such as gravitational collapse, gravitational waves and other phenomena associated with strong gravitational fields. This special session will encourage further collaborative research into these topics and also draw young talent to this field. The participation of graduate students and young Ph.D.'s will ensure the continued vitality of the discipline.