Topology of Manifolds, C*-Algebras, and Applications
流形拓扑、C*-代数及其应用
基本信息
- 批准号:0504212
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2005
- 资助国家:美国
- 起止时间:2005-06-01 至 2009-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Proposed abstract:Professor Jonathan Rosenberg will study the topology and geometry of manifolds, as well as C*-algebraic index theory, and various applications. The applications will include a number of topics relevant to modern physics,such as the classification of manifolds of positive scalar curvature,relevant to the problem of understanding the possibilities for thelarge-scale geometry of space-time, and questions relevant to dualities between different space-time topologies in string theory. Professor Rosenberg is closely involved in the supervision and improvement of the mathematics graduate programs at the University of Maryland. He will train graduate students and advanced undergraduate students in algebra, analysis, geometry, topology, and mathematical physics, and will also work toward integration of mathematical software into the undergraduate mathematics curriculum.In more detail, one main focus of the proposal will be the classification of manifolds via their Yamabe invariants, and the classification of metrics of positive scalar curvature, problems which involve a quite subtle blend of differential topology, differential geometry, and analysis. Another focus will be applications of topology and noncommutative geometry to mathematical physics, especially to T-duality in string theory. Other topics will include the use of invariants coming from C*-algebras (especially Kasparov's KK-theory) to study the geometry and topology of manifolds. For example, the KK-classes coming from the classical elliptic operators, such as the signature operator and the Dolbeault operator, will be intensively studied. These studies will deepen the link between topological and analytic approaches to geometry of manifolds and singular spaces. In addition, Professor Rosenberg will study the applications of K-theory to the study of C*-algebras, and various related problems on algebraic K-theory, especially concerning algebras of operators or algebras coming from quantization of geometrical systems.
建议摘要:Jonathan Rosenberg教授将研究流形的拓扑和几何,以及C*-代数指数理论和各种应用。 这些应用将包括一些与现代物理学相关的主题,例如正标量曲率流形的分类,与理解时空大尺度几何的可能性有关的问题,以及与弦论中不同时空拓扑之间的对偶有关的问题。 罗森伯格教授密切参与监督和改进数学研究生课程在马里兰州的大学。他将在代数、分析、几何、拓扑和数学物理方面对研究生和高级本科生进行培训,并将致力于将数学软件整合到本科数学课程中。更详细地说,该提案的一个主要重点是通过Yamabe不变量对流形进行分类,以及对正标量曲率度量进行分类,这些问题涉及微分拓扑学、微分几何学和分析学的微妙结合。另一个重点将是应用拓扑和非交换几何的数学物理,特别是T-对偶弦理论。其他主题将包括使用来自C*-代数(特别是卡斯帕罗夫的KK-理论)的不变量来研究流形的几何和拓扑。例如,来自经典椭圆算子的KK-类,如签名算子和Dolbeault算子,将被深入研究。这些研究将加深流形和奇异空间几何的拓扑和解析方法之间的联系。此外,Rosenberg教授将研究K-理论在C*-代数研究中的应用,以及代数K-理论的各种相关问题,特别是关于算子代数或来自几何系统量子化的代数。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Jonathan Rosenberg其他文献
A quick proof of Harish-Chandra’s Plancherel theorem for spherical functions on a semisimple Lie group
半单李群上球函数 Harish-Chandra Plancherel 定理的快速证明
- DOI:
10.1090/s0002-9939-1977-0507231-8 - 发表时间:
1977 - 期刊:
- 影响因子:1.3
- 作者:
Jonathan Rosenberg - 通讯作者:
Jonathan Rosenberg
The Kunneth Theorem and the Universal Coefficient Theorem for Equivariant K-Theory and Kk-Theory
等变 K 理论和 Kk 理论的 Kunneth 定理和通用系数定理
- DOI:
- 发表时间:
1986 - 期刊:
- 影响因子:0
- 作者:
Jonathan Rosenberg;Claude L. Schochet - 通讯作者:
Claude L. Schochet
Positive scalar curvature on manifolds with fibered singularities
具有纤维奇点的流形上的正标量曲率
- DOI:
- 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
B. Botvinnik;Jonathan Rosenberg - 通讯作者:
Jonathan Rosenberg
Algebraic K -theory and derived equivalences suggested by T-duality for torus orientifolds
东方环面 T-对偶性提出的代数 K 理论和导出等价
- DOI:
- 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
Jonathan Rosenberg - 通讯作者:
Jonathan Rosenberg
T-Duality for Orientifolds and Twisted KR-Theory
Orientifolds 的 T 对偶性和扭曲的 KR 理论
- DOI:
- 发表时间:
2014 - 期刊:
- 影响因子:1.2
- 作者:
Charles F. Doran;S. Méndez;Jonathan Rosenberg - 通讯作者:
Jonathan Rosenberg
Jonathan Rosenberg的其他文献
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{{ truncateString('Jonathan Rosenberg', 18)}}的其他基金
Topology, Noncommutative Geometry, and Mathematical Physics
拓扑学、非交换几何和数学物理
- 批准号:
1607162 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Continuing Grant
Focus Program on Noncommutative Geometry and Quantum Groups; June 3-28, 2013 at the Fields Institute in Toronto, Canada
非交换几何和量子群重点项目;
- 批准号:
1266158 - 财政年份:2013
- 资助金额:
-- - 项目类别:
Standard Grant
Topology, Noncommutative Geometry, and Mathematical Physics
拓扑学、非交换几何和数学物理
- 批准号:
1206159 - 财政年份:2012
- 资助金额:
-- - 项目类别:
Continuing Grant
Topology, Noncommutative Geometry, and Applications
拓扑、非交换几何及其应用
- 批准号:
0805003 - 财政年份:2008
- 资助金额:
-- - 项目类别:
Continuing Grant
Manifolds and C*-Algebraic Index Theory
流形和 C*-代数指数理论
- 批准号:
0103647 - 财政年份:2001
- 资助金额:
-- - 项目类别:
Continuing Grant
Comparative Ecosystem Management and Local Participation
比较生态系统管理和地方参与
- 批准号:
9725600 - 财政年份:1998
- 资助金额:
-- - 项目类别:
Standard Grant
Mathematical Sciences: Special Year in Geometry
数学科学:几何特别年
- 批准号:
8911101 - 财政年份:1989
- 资助金额:
-- - 项目类别:
Standard Grant
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