Two areas in particular seem suitable for further study in then general field of understanding Cosmological Dark-Matter Profiles. Certain classical analytic solutions to the cosmological in fall are well-known and a first task would be to extend these exact classical solutions to more modern cosmological models and more general geometries. Then, recent very massive and high-resolution simulations would be analyzed to determine the applicability of the analytic solutions. Should the results be promising, they could be compared to real observational data. A second and closely related project is to try to understand the central profiles of dark matter halos, which are approximately power laws with asymptotic slopes found to be in the range of 1.0to 1.5. The true nature and origin of these profiles remains an unsolved problem. We plan to study these profiles using simplified models of mergers of halos, as well as statistical physics tools. Again analytic work would be compared with recent numerical simulations, and observational constraints. The institute of Astronomy is a department of the University of Cambridge, comprising 20 permanent academic staff, 60 post-doctoral research staff and 50 PhD students. Cambridge has the largest astronomy and astrophysics research community in the UK and the Institute has close links with the nearby Cavendish Astrophysics Group and the Department of Applied Mathematics and Theoretical Physics. The thriving scientific atmosphere is reflected in a busy programme of seminars and colloquia given by international, national and local astronomers. Dr. Arad would work closely with the Cosmology group at the Institute of Astronomy, primarily with Professor J. P. Ostriker, but also interacting with Professors' G Efstathiou, O. Lahav and M.Rees. There are numerous post-doctoral fellows and visitors working in related areas, as well as faculty at DAMTP, such as Professor N.Turok.