Collaborative Research: The Mathematics of Stochastic Gravitational Lensing: Applications to Flux Ratio Anomalies and Dark Matter

这是一个跨学科的研究项目，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反常问题，以及冷暗物质图像的困难。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，以及研究随机放大漂移集的统计几何。研究结果将被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。这项研究还在几个美国机构和德国波茨坦建立了科学合作伙伴关系。

AST-0434277PettersThis 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.