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-0305505TITLE：“几何和物理学”摘要是该赠款支持的三个个人研究人员。教授和各种合着者研究首先扭曲了K理论和循环群，其次是Dirac运算符的差异K理论和几何不变，最后是M-Bhey and String理论的异常。 Hauselresearch教授在Quaternionic几何形状中进行了新的数学，该数学与复杂几何形状中的已知数学相对应，例如Higgsbundles的模量空间，方形可集成的谐波形式，集成在Circle CompactManifolds上，并在增生平面布置的面部矢量上进行。 Uhlenbeckhas教授在双曲程方程上进行了两个项目，这是找到协变量波动算子的基本原理之一，以及一个在两个空间维度中研究的波浪块。她还研究了TCFT中的Virasoro行动。三个支持的研究人员是一个大型几何组的一部分WhoseReSearch项目涵盖了许多几何主题，这些主题源于高能理论理论物理学或工程物理学。在数学中，该小组的工作不仅限于几何分析，还涉及钙化的几何形状，几何拓扑，代数拓扑，表示理论，谐波分析和数学物理学。对GrouPresearch的必不可少的是具有不同背景插入式，物理学和生物学的数学家之间的合作。