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Geometry and Physics

几何与物理

基本信息

批准号：
0305505
负责人：
Daniel Freed
金额：
$ 34.52万
依托单位：
University of Texas at Austin
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2003
资助国家：
美国
起止时间：
2003-08-15 至 2007-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0305505&HistoricalAwards=false
关键词：
Geometry Physics

项目摘要

Proposal DMS-0305505Title: "Geometry and Physics"ABSTRACTThere are three individual researchers supported on this grant. ProfessorFreed and various coauthors study first twisted K-theory and loop groups,secondly differential K-theory and geometric invariants of Dirac operators,and finally anomalies in M-theory and string theory. Professor Hauselresearches new mathematics in quaternionic geometry which corresponds toknown mathematics in complex geometry, such as the moduli space of Higgsbundles, square integrable harmonic forms, integration on circle compactmanifolds and face vectors of hyperplane arrangements. Professor Uhlenbeckhas two projects on hyperbolic equations, one of finding fundamentalsolutions of covariant-derivative wave operators and one studying wave mapblow-up in two space dimensions. She also studies Virasoro actions in TCFT.The three supported researchers are part of a large geometry group whoseresearch projects span many topics in geometry which originate in high energytheoretical physics or engineering physics. In mathematics proper the workof the group is not limited to geometric analysis, but also involvesalgebraic geometry, geometric topology, algebraic topology, representationtheory, harmonic analysis, and mathematical physics. Essential to the groupresearch are collaborations among mathematicians with diverse backgrounds inmathematics, physics and biology.

提案DMS-0305505标题：“几何与物理“摘要有三个独立的研究人员支持这项赠款。ProfessorFreed和各种合著者研究第一扭曲的K-理论和循环群，其次是微分K-理论和几何不变的狄拉克算子，最后异常M-理论和弦理论。Hausel教授研究四元数几何中的新数学，这与复杂几何中的已知数学相对应，例如Higgsbundles的模空间，平方可积调和形式，圆紧流形上的积分和超平面安排的面向量。 Uhlenbeck教授有两个关于双曲方程的项目，一个是寻找协变导数波算子的基本解，另一个是研究二维空间中的波映射爆破。她还研究了TCFT中的Virasoro行为。这三位受资助的研究人员是一个大型几何小组的一部分，该小组的研究项目涵盖了几何中的许多主题，这些主题源于高能理论物理或工程物理。在数学正确的工作组不仅限于几何分析，而且还涉及代数几何，几何拓扑，代数拓扑，representationtheory，调和分析，和数学物理。对于团体来说，具有不同数学、物理和生物学背景的数学家之间的合作是必不可少的。