Special Session on Mathematical Relativity at CADS 5

爱因斯坦方程在过去几年中取得了非凡的发展，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，准局部质量，初始数据集变形和边缘捕获表面性质的理解的进步。与其他几何偏微分方程的卓有成效的联系，如杨米尔斯、波图、山部方程、各种抛物线流，以及与其他附近领域的联系，如谐波分析，导致了一系列令人兴奋的新发现。这一活动吸引了许多几何分析人员关注所开发的几何技术的丰富问题和潜在应用。5月22日至26日，在以色列Akko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领域的顶尖专家和年轻研究人员，讨论这些问题和最近的结果，以促进合作和进一步的进展。随着相对论引力物理实验项目的推进，建立丰富的理论模型显得尤为重要。为了确保数学相对论继续对实验工作产生强烈的影响，并与之相互作用，这些模型应该成熟，并能够对一些主题做出定量预测，如引力坍缩、引力波和其他与强引力场相关的现象。本次特别会议将鼓励对这些主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将确保该学科的持续活力。

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.