This is a proposal to harness the special resources at Stony Brook to train students and post-docs in geometry and its interaction with mathematical physics. The plan involves a radical shift from standard curricula and should be broadly appealing to young people who are considering the possibility of a career in mathematics.
Stony Brook has a large, highly active (and interactive) group of geometers representing nearly all aspects of the field from algebraic geometry to string topology. A substantial part of the research of this group is related to and/or inspired by modern physics, and there is a long tradition of interaction between Stony Brook's mathematicians and physicists. This is represented in collaborations, seminars, joint students, and conferences, as well as two major programs in mathematics and physics, funded outside the NSF. This is a proposal to use these resources in new, effective ways for the training of young researchers.
The proposal aims at: (1) incorporating the high-level seminars and workshops into the training of students at an early point by close mentoring, (2) bringing students more quickly and effectively to the research level, (3) training students and post-docs in the dual cultures of geometry and physics, (4) giving undergraduates a taste of mathematical research at the interactive level.
If successful this could lead to an adoption of new models for undergraduate development and graduate education. It should produce more effective researchers and therefore lead to better careers in mathematics. A fundamental outcome would be the attraction of more U.S. citizens into mathematics in general and these fields in particular, because this program offers close personal supervision, an interactive and challenging environment and strong intellectual appeal. Another important outcome would be a new generation trained from the beginning in the dual cultures of mathematics and physics. This should lead to even greater communication between these fields in the future.
