A walk in the noncommutative garden

Abstract

This text is written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It gives a survey of methods and results in noncommutative geometry, based on a discussion of significant examples of noncommutative spaces in geometry, number theory, and physics. The paper also contains an outline (the "Tehran program") of ongoing joint work with Consani on the noncommutative geometry of the adeles class space and its relation to number theoretic questions.

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