Summer school on Noncommutative geometry

Northwestern University, Evanston IL

Investigators

Abstract

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the classical methods of studying spaces to the noncommutative case, i.e. to the situation where the identity xy=yx is no longer valid.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