This award provides partial support for two editions of a series of summer schools on Geometry and Physics (GAP). GAP VIII (2010) will concentrate on differential geometric aspects of noncommutative geometry, while GAP IX (2011) will be devoted to algebraic geometric aspects of noncommutative geometry and mathematical physics. Noncommutative geometry aims to study geometric properties of a new class of "spaces" whose algebras of functions are no longer commutative. The central idea goes back to quantum mechanics, in which observables such as position and momentum do not commute. The subject has undergone tremendous exploration recently due to its close connection to a number of areas of mathematics and mathematical physics, including foliation theory, index theory, representation theory, algebraic geometry, quantum field theory, quantization theory, and string theory.
The project consists in a pair of summer schools (GAP VIII and GAP XI) aimed at gathering different streams and instances of noncommutative geometry, as well as identifying new emerging directions. The main purposes of the proposed activities are to bring together leading experts and young researchers working in rapidly developing subjects, and to promote interaction between mathematicians and physicists, and groups working on different aspects of related areas so as to foster interaction, encourage cross-fertilization between different fields, and promote the dissemination of the most recent results of current research. There are many talented young people working in this area. GAP VIII and GAP XI will provide them with excellent opportunities to disseminate their ideas and to broaden their perspective. The PIs anticipate inviting a substantial number of mathematicians at the postdoctoral and graduate student level (from Europe, the United States, and developing countries), and holding poster or short-talk sessions through which young researchers will be given the chance to present their work. The schools will provide an excellent opportunity for young American scientists to exchange ideas with their European peers and initiate collaborations.
This project is jointly funded by the Geometric Analysis Program, the Algebra and Number Theory Program, and the Analysis Program.
