Collaborative Research: The Mathematics of Stochastic Gravitational

合作研究：随机引力数学

• 批准号: 0433809
• 负责人: Paul Schechter
• 金额: $ 20万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2007-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0433809&HistoricalAwards=false
• 关键词: Collaborative; Research; Mathematics; Stochastic; Gravitational

AST-0433809SchechterThis is an interdisciplinary research program involving synergistic interactions between mathematics (probability theory, statistics, singularity theory) and astronomy (gravitational lensing of quasars, dark matter on galactic scales). This research addresses two pressing scientific issues: the flux ratio anomaly problem in gravitational lensing, and difficulties with the cold dark matter picture. It will open up new mathematical directions, including a generalization of Morse theory to a stochastic setting, and a study of the statistical geometry of random magnification excursions sets.Results from the research will be incorporated into an undergraduate seminar on the mathematics of gravitational lensing and a graduate course on general relativity, and presented at major international scientific conferences. This study also creates scientific partnerships among several US institutions and Potsdam, Germany.

AST-0433809 Schechter这是一个跨学科的研究计划，涉及数学（概率论，统计学，奇点理论）和天文学（类星体的引力透镜，星系尺度上的暗物质）之间的协同作用。 这项研究解决了两个紧迫的科学问题：引力透镜中的通量比异常问题，以及冷暗物质图片的困难。 它将开辟新的数学方向，包括将莫尔斯理论推广到随机环境，以及研究随机放大偏移集的统计几何。研究结果将纳入关于引力透镜数学的本科生研讨会和关于广义相对论的研究生课程，并在主要的国际科学会议上发表。 这项研究还在美国的几个机构和德国的波茨坦之间建立了科学伙伴关系。