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A walk in the noncommutative garden

Alain Connes·Matilde Marcolli
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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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Alain Connes, Matilde Marcolli. 2006-01-03. A walk in the noncommutative garden. https://arxiv.org/abs/math/0601054

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