An informal introduction to the ideas and concepts of noncommutative geometry
by Thierry Masson
Publisher: arXiv 2006
Number of pages: 56
This informal introduction is an extended version of a three hours lecture given at the 6th Peyresq meeting "Integrable systems and quantum field theory". In this text, we make an overview of some of the mathematical results which motivated the development of what is called noncommutative geometry.
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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.
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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.