Summer school on Noncommutative geometry

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。它将包括八个讲座课程的领先专家涵盖非交换几何的基础知识（K理论，指数理论，变形量子化，量子群）以及最近的发展，在这个问题上，并在其连接到其他领域，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。非交换几何是数学的主题，它推广了经典的研究方法，空间到非交换的情况，即到恒等式xy=yx不再有效的情况。这种推广在许多应用中都需要：量子物理学（非对易性是海森堡测不准原理的数学表现）;几何学、微分方程理论、拓扑学等（空间或另一个系统的对称性不对易，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，要发展非对易几何的方法本身，人们需要代数、几何和拓扑学的高级技术，这些技术在很大程度上受到数学物理的启发。该学院将汇集该领域的顶尖专家，以及来自美国，美洲和欧洲的许多年轻研究人员。

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the classical methods of studying spaces to the noncommutative case, i.e. to the situation where the identity xy=yx is no longer valid.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