Research Training in Geometry at the Interface with Physics

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This is a proposal to harness the special resources at StonyBrook to train students and post-docs in geometry and itsinteraction with mathematical physics. The plan involves aradical shift from standard curricula and should be broadlyappealing to young people who are considering the possibility of acareer in mathematics.Stony Brook has a large, highly active (and interactive) groupof geometers representing nearly all aspects of the fieldfrom algebraic geometry to string topology.A substantial part of the research of this group is related to and/orinspired by modern physics, and there is a long tradition ofinteraction between Stony Brook's mathematicians and physicists. This isrepresented in collaborations, seminars, joint students, andconferences, as well as two major programs in mathematics andphysics, funded outside the NSF. This is a proposal to use theseresources in new, effective ways for the training of young researchers.The proposal aims at: (1) incorporating the high-level seminars andworkshops into the training of students at an early point by closementoring, (2) bringing students more quickly and effectively to theresearch level, (3) training students and post-docs in the dual culturesof geometry and physics, (4) giving undergraduates a taste ofmathematical research at the interactive level.If successful this could lead to an adoption of new models forundergraduate development and graduate education. It should producemore effective researchers and therefore lead to better careersin mathematics. A fundamental outcome would be the attraction of moreU.S. citizens into mathematics in general and these fields inparticular, because this program offers close personal supervision, an interactive and challenging environment and strong intellectualappeal. Another important outcome would be a new generation trainedfrom the beginning in the dual cultures of mathematics and physics.This should lead to even greater communication between these fields inthe future.