Henri Moscovici

Masoud Khalkhali

Guoliang Yu

Nigel Higson

Caterina Consani

Ali Chamseddine

This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.

On the Occasion of Alain Connes' 70th Birthday

Advances in Noncommutative Geometry

Alain Connes

Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.

Proceedings of the Twenty-First Meeting of the Japan-U.S. Mathematics Institute

Noncommutative Geometry, Arithmetic, and Related Topics

Matilde Marcolli

In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Where Arithmetic meets Geometry and Physics

Noncommutative Geometry and Number Theory

Caterina Consani

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