Noncommutative Geometry at the Newton Institute
牛顿研究所的非交换几何
基本信息
- 批准号:0611653
- 负责人:
- 金额:$ 1.94万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2006
- 资助国家:美国
- 起止时间:2006-06-01 至 2007-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This award is for partial support of US participants in a semester long workshop at the Newton Institute, Cambridge, UK, in noncommutative geometry for the period July 24 through December 22, 2006. Noncommutative geometry aims to carry over geometrical concepts to a new class of spaces whose algebras of functions are no longer commutative. The central idea goes back to quantum mechanics, where classical observables such as position and momenta no longer commute. In recent years it has become appreciated that such noncommutative spaces retain a rich topology and geometry expressed first of all in K-theory and K-homology, as well as in finer aspects of the theory. The subject has also been approached from a more algebraic side with the advent of quantum groups and their quantum homogeneous spaces. The subject in its modern form has also been connected with developments in several different fields of both pure mathematics and mathematical physics. In mathematics these include fruitful interactions with analysis, number theory, category theory and representation theory. In mathematical physics, developments include the quantum Hall effect, applications to the standard model in particle physics and to renormalization in quantum field theory, models of spacetimes with noncommuting coordinates. Noncommutative geometry also appears naturally in string/M-theory. The program will be devoted to bringing together these different streams and instances of noncommutative geometry, as well as identifying new emerging directions. Three main themes of the program will be reflected in workshops in July, September and December of 2006, covering noncommutative geometry and cyclic cohomology, noncommutative geometry and fundamental physics, and new directions in noncommutative geometry respectively.
该奖项是为了部分支持美国参与者在一个学期长的研讨会在牛顿研究所,剑桥,英国,在非交换几何的期间2006年7月24日至12月22日。非交换几何的目的是将几何概念带到一类新的空间,其函数代数不再是交换的。其中心思想可以追溯到量子力学,在量子力学中,位置和动量等经典的可观测量不再互换。 近年来,人们已经认识到,这种非交换空间保留了丰富的拓扑和几何表示,首先在K-理论和K-同调,以及在更精细的方面的理论。随着量子群和它们的量子齐性空间的出现,这个问题也从更代数的角度被探讨。这个问题在其现代形式也已与发展中的几个不同领域的纯数学和数学物理。在数学中,这些包括与分析,数论,范畴论和表示论的富有成效的相互作用。在数学物理学中,发展包括量子霍尔效应,粒子物理学中标准模型的应用,量子场论中的重整化,非对易坐标时空模型。非对易几何也自然地出现在弦/M理论中。该计划将致力于汇集这些不同的流和非交换几何的实例,以及确定新的新兴方向。 该计划的三个主题将反映在2006年7月,9月和12月的研讨会,分别涵盖非交换几何和循环上同调,非交换几何和基础物理,以及非交换几何的新方向。
项目成果
期刊论文数量(0)
专著数量(0)
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会议论文数量(0)
专利数量(0)
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John Roe其他文献
The epidemiology of sports and leisure-related injury hospitalisations in Queensland: A five-year review
- DOI:
10.1016/j.injury.2023.04.035 - 发表时间:
2023-06-01 - 期刊:
- 影响因子:
- 作者:
Daniel Brimm;John Roe;Jacelle Warren;Tanya Smyth;Kirsten Vallmuur;Shahera Banu - 通讯作者:
Shahera Banu
Basic Noncommutative Geometry by Masoud Khalkhali
- DOI:
10.1007/s00283-014-9489-6 - 发表时间:
2014-12-17 - 期刊:
- 影响因子:0.400
- 作者:
John Roe - 通讯作者:
John Roe
John Roe的其他文献
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