This quantity represents the complaints of the convention on themes in Deformation Quantization and Non-Commutative constructions held in Mexico urban in September 2005. It includes survey papers and unique contributions by means of quite a few specialists within the fields of deformation quantization and non-commutative derived algebraic geometry within the interface among arithmetic and physics. It additionally comprises a piece of writing in keeping with the XI Memorial Lectures given through M. Kontsevich, that have been added as a part of the convention. this is often an exceptional introductory quantity for readers drawn to studying approximately quantization as deformation, Hopf algebras, and Hodge buildings within the framework of non-commutative algebraic geometry.
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