This 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.
