Surveys in Noncommutative Geometry
by Nigel Higson, John Roe
Publisher: American Mathematical Society 2006
Number of pages: 208
The series of expository lectures intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Topics: applications of noncommutative geometry to problems in ordinary geometry and topology, Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory, residue index theorem of Connes and Moscovici, etc.
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by Travis Schedler - arXiv
In these notes, we give an example-motivated review of the deformation theory of associative algebras in terms of the Hochschild cochain complex as well as quantization of Poisson structures, and Kontsevich's formality theorem in the smooth setting.
by Thierry Masson - arXiv
This is an extended version of a three hours lecture given at the 6th Peyresq meeting 'Integrable systems and quantum field theory'. We make an overview of some of the mathematical results which motivated the development of noncommutative geometry.
by Alain Connes - Academic Press
The definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics. Ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics.
by D. Kaledin
The first seven lectures deal with the homological part of the story (cyclic homology, its various definitions, various additional structures it possesses). Then there are four lectures centered around Hochschild cohomology and the formality theorem.