The lecture notes of this course at the EMS Summer School on Noncommutative Geometry and Applications in September, are now published by the EMS. Here are the contents, preface and updated bibliography from the published book. Contents 1 Commutative Geometry from the Noncommutative Point of View The Gelfand–Na˘ımark cofunctors. Noncommutative geometry and Quantum physics on manifolds with boundary T.R. Govindarajan Chennai Mathematical Institute, Chennai Quantum theory on manifolds with boundary present novel features due to boundary conditions. There are edge states localised at the boundary. Noncommutative rings resemble rings of matrices in many respects. Following the model of algebraic geometry, attempts have been made recently at defining noncommutative geometry based on noncommutative rings. Noncommutative rings and associative algebras (rings that are also vector spaces) are often studied via their categories of modules. A module over a ring is an abelian group . "Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject.

Objectives This is the third Shanghai workshop on Noncommutative Algebraic geometry. The conference emphasizes on most significant developments, new research directions and interactions with other fields such as noncommutative algebra, representation theory, algebraic geometry, and mathematical physics. PDF | The structure of a manifold can be encoded in the commutative algebra of functions on the manifold it self - this is usual -. In the case of a non | Find, read and cite all the research. Lecture Febru Introduction to spectral triples in noncommutative geometry, real structures, Morita equivalence and inner fluctuations, the Left-Right symmetric algebra Lecture Febru Odd bimodules, representations of the left-right symmetric algebra, generations and particles as basis elements, real structure and. I took a course last year on noncommutative geometry (which kind of turned out to be a whole lot of homological algebra). I get that we want to come up with some sort of geometric perspective on noncommutative rings and algebras like we have for commutative ones ({commutative rings} {affine schemes}, {commutative C*-algebras} {compact Hausdorff spaces}), and that at the moment.