This quantity represents the complaints of the convention on issues in Deformation Quantization and Non-Commutative constructions held in Mexico urban in September 2005. It includes survey papers and unique contributions through a variety of specialists within the fields of deformation quantization and non-commutative derived algebraic geometry within the interface among arithmetic and physics. It additionally comprises an editorial in response to the XI Memorial Lectures given via M. Kontsevich, that have been introduced as a part of the convention. this is often an exceptional introductory quantity for readers attracted to studying approximately quantization as deformation, Hopf algebras, and Hodge constructions within the framework of non-commutative algebraic geometry.
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