The School of Mathematics was formed in 1930 at the founding of the Institute for Advanced Study, and many mathematical institutes founded both in the United States and abroad in the intervening decades were inspired by a desire to emulate the School and its achievements. The original purpose of the Institute was to provide an environment exceptionally favorable for research by freeing scholars from teaching duties and by offering total freedom in research plans and objectives. More recently, a new goal of the Institute has been to provide a post doctoral education for junior Ph.D.'s. Although the School of Mathematics, as a part of the Institute, has a substantial endowment which is adequate for the permanent faculty and the maintenance of an exceptionally agreeable working environment, it does not suffice to support all the temporary members. This grant will provide support to allow about 26 junior mathematicians to spend a year at the School of Mathematics.