This award by the National Science Foundation provides core support to the Mathematical Sciences Research Institute located at Berkeley, California. The fundamental goal of the Mathematical Sciences Research Institute (MSRI) is to stimulate and invigorate research in the mathematical sciences by bringing together, in a programmatically focused scientific environment, the top mathematical scientists nationally and internationally in given research subjects. The interaction of senior and mid-level scholars and the very best postdoctoral fellows in a given field produces an intensely stimulating and exciting environment where new ideas can be exploited and developed. The MSRI places a high priority on the training of postdoctoral researchers, and the scientific structure and budgetary allocations of funds reflect this commitment. Normally, two academic-year scientific research programs take place each year. In addition to these academic year programs, the MSRI conducts workshops, conferences, and microprograms which complement the year-long activities. The MSRI also supports summer research and training programs for graduate students. Every effort is made to schedule programs of timely research interest and opportunities exist for cross-programmatic collaboration and scientific exchange.