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

AbstractAward：DMS-9820748首席研究员：戴贤哲和叶汝刚该奖项为将于1999年7月21日至7月24日在加州圣巴巴拉大学校园举行的（第一届）圣巴巴拉夏季几何会议提供部分支持。这次会议的目的有三个。第一，把几何学，特别是与物理学密切相关的领域的顶尖专家聚集在一起。第二，综述物理学，特别是弦论所推动的最近的显著进展，并为研究生、研究生和博士后指出新的方向和前沿。第三，进一步促进数学和物理之间富有成效的互动，与本次会议后在UCSB理论物理研究所举办的“几何与对偶“项目相协调。目前，我们正在见证物理（特别是高能物理）和数学（特别是微分几何，微分拓扑和代数几何）之间互动的黄金时代。一方面，物理学家在物理直觉的指导下，借助最先进的数学工具，带来了新的突破，提出了新的挑战性问题，也为数学提供了新的见解。另一方面，数学家在物理学进步的启发和激励下，在数学方面取得了惊人的进展，这反过来又为物理学家提供了新的机器。 数学家也与物理学家合作对物理学做出直接贡献.物理学家和数学家的共同努力使我们对宇宙结构的理解取得了重大进展，并将最终发现主要的新能源，并为更高和更深层次的更强大的自然计算提供新的基础。 圣巴巴拉夏季几何会议旨在为这些发展做出贡献。

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.