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the classical methods of studying spaces to the noncommutative case, i.e. to the situation where the identity xy=yx is no longer valid.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.

非对易几何学校将于2010年7月26日至8月7日在阿根廷布宜诺斯艾利斯举行。它将包括八门主要专家的讲座课程，涵盖非对易几何的基础知识(K-理论、指数理论、形变量子化、量子群)以及该学科的最新发展及其与其他领域的联系，如拓扑量子场论、辛几何、顶点算子代数和其他数学物理主题。非对易几何是将研究空间的经典方法推广到非对易情形的数学学科，即恒等式xy=yx不再有效的情况。许多应用都需要这种推广：量子物理(其中非交换性是海森伯格测不准原理的数学表现)；几何学、微分方程式理论、拓扑学等(一个空间或另一个系统的对称性是不交换的，即如果一个人以不同的顺序应用两个对称性，就会得到不同的结果)。也许不那么直观的是，为了发展非对易几何方法本身，人们需要在很大程度上受到数学物理启发的代数、几何和拓扑学的高级技术。该学院将汇集该领域以及邻近学科的顶尖专家，以及来自美国、美洲和欧洲的许多年轻研究人员。