Santa Barbara Summer Conference in Geometry, July 21-24, 1999, Santa Barbara, California

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AbstractAward: DMS-9820748Principal Investigator: Xianzhe Dai and Rugang YeThis award provides partial support for the (first) Santa BarbaraSummer Conference in Geometry, to be held from July 21 to July24, 1999 on the campus of University of California, SantaBarbara. The purposes of this conference are threefold. First, tobring together the leading experts in geometry, and especially inthe fields closely related to physics. Second, to survey therecent remarkable progress spurred by physics, especially stringtheory, and point to new directions and frontiers for youngresearchers, graduate students and postdocs. Third, to furtherstimulate the fruitful interactions between mathematics andphysics in coordination with the program "Geometry and Duality"to be run right after this conference at the Institute forTheoretical Physics, UCSB.Currently, we are witnessing the blossoming of a golden age ofinteractions between physics (in particular high energy physics)and mathematics (in particular, differential geometry,differential topology and algebraic geometry). On the one hand,physicists, guided by physical intuitions and equipped with mostadvanced mathematical tools, bring about new break-throughs whichpose new challenging problems and also provide new insights formathematics. On the other hand, mathematicians, inspired andspurred by advances in physics, make amazing progresses inmathematics, which in turn provide new machineries forphysicists. Mathematicians also make direct contributions tophysics in collaboration with physicists. The joint efforts ofphysicists and mathematicians lead to major advances in ourunderstanding of the structures of the universe, and willultimately uncover major new energy sources and provide newfoundations for more powerful natural computations at higher anddeeper levels. The Santa Barbara Summer Conference in Geometryis designed to make contributions in the framework of thesedevelopments.