Summer school on Noncommutative geometry

非交换几何暑期学校

• 批准号: 1041576
• 负责人: Boris Tsygan
• 金额: $ 2.5万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-08-01 至 2012-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1041576&HistoricalAwards=false
• 关键词: Summer; Noncommutative; geometry

The school on noncommutative geometry will take place in Buenos Aires, Argentina, on July 26-August 7, 2010. It will include eight lecture courses by leading experts covering the basics of noncommutative geometry (K-theory, index theory, deformation quantization, quantum groups) as well as most recent developments in the subject and in its connections to other fields, such as topological quantum field theory, symplectic geometry, vertex operator algebras and other topics of mathematical physics.Noncommutative geometry is the subject of mathematics that generalizes the classical methods of studying spaces to the noncommutative case, i.e. to the situation where the identity xy=yx is no longer valid. This generalization is needed for many applications: quantum physics (where noncomutativity is a mathematical manifestation of the Heisenberg uncertainty principle); geometry, theory of differential equations, topology, etc. (where symmetries of a space or of another system do not commute, i.e. one gets different results if one applies two symmetries in different orders). Perhaps less intuitively, to develop the methods of noncommutative geometry themselves, one needs advanced techniques of algebra, geometry, and topology that are inspired to a large extent by mathematical physics. The school will bring together the leading experts in the field, as well as in the adjacent subjects, with hmany young researchers from the US, the Americas, and Europe.

非交换几何学校将于 2010 年 7 月 26 日至 8 月 7 日在阿根廷布宜诺斯艾利斯举行。它将包括由顶尖专家讲授的八门讲座课程，涵盖非交换几何的基础知识（K 理论、索引理论、形变量子化、量子群）以及该学科及其与其他领域的联系的最新发展，例如拓扑量子场论、辛几何、 顶点算子代数和数学物理的其他主题。非交换几何是一门数学学科，它将研究空间的经典方法推广到非交换情况，即恒等式 xy=yx 不再有效的情况。许多应用都需要这种概括：量子物理学（其中非交换性是海森堡不确定性原理的数学表现）；几何、微分方程理论、拓扑等（其中空间或另一个系统的对称性不交换，即，如果以不同的顺序应用两种对称性，则会得到不同的结果）。也许不太直观的是，为了开发非交换几何本身的方法，我们需要先进的代数、几何和拓扑技术，这些技术在很大程度上受到数学物理学的启发。该学院将汇集该领域以及相关学科的领先专家以及来自美国、美洲和欧洲的许多年轻研究人员。