Geometry and Physics

几何与物理

• 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

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 此项资助支持三名个人研究人员。 Freed教授和多位合著者首先研究扭曲K理论和环群，其次研究微分K理论和狄拉克算子的几何不变量，最后研究M理论和弦理论中的异常。豪塞尔教授研究四元几何中的新数学，这些数学对应于复杂几何中的已知数学，例如希格斯丛的模空间、平方可积调和形式、圆紧流形上的积分以及超平面排列的面向量。 Uhlenbeck 教授有两个关于双曲方程的项目，其中之一是寻找协变导数波算子的基本解，另一项是研究二维空间中的波图放大。她还在 TCFT 中研究 Virasoro 行为。这三位受资助的研究人员是一个大型几何小组的成员，该小组的研究项目涵盖几何学中的许多主题，这些主题源自高能理论物理或工程物理。 在数学本身，该小组的工作不仅限于几何分析，还涉及代数几何、几何拓扑、代数拓扑、表示论、调和分析和数学物理。 小组研究的关键是具有不同数学、物理和生物学背景的数学家之间的合作。