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Quanta of Maths
Edited by: Etienne Blanchard, University of Paris 7, France, David Ellwood, Clay Mathematics Institute, Cambridge, MA, Masoud Khalkhali, University of Western Ontario, London, ON, Canada, Matilde Marcolli, California Institute of Technology, Pasadena, CA, Henri Moscovici, Ohio State University, Columbus, OH, and Sorin Popa, University of California, Los Angeles, CA
A co-publication of the AMS and Clay Mathematics Institute.
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Clay Mathematics Proceedings
2010; 675 pp; softcover
Volume: 11
ISBN-10: 0-8218-5203-5
ISBN-13: 978-0-8218-5203-3
List Price: US$129
Member Price: US$103.20
Order Code: CMIP/11
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See also:

The Algebraic and Geometric Theory of Quadratic Forms - Richard Elman, Nikita Karpenko and Alexander Merkurjev

Surveys in Noncommutative Geometry - Nigel Higson and John Roe

Arithmetic Noncommutative Geometry - Matilde Marcolli

The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics.

Specific themes covered by the articles are as follows:

  • entropy in operator algebras, regular \(C^*\)-algebras of integral domains, properly infinite \(C^*\)-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces;
  • von Neumann algebras, fundamental Group of \(\mathrm{II}_1\) factors, subfactors and planar algebras;
  • Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory;
  • cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem;
  • noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras;
  • Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities;
  • cyclotomy and analytic geometry over \(F_1\), quantum modular forms;
  • differential K-theory, cyclic theory and S-cohomology.

Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

Readership

Graduate students and research mathematicians interested in recent developments in various areas of mathematics.

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