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Quanta of Maths

Edited by: Etienne Blanchard University of Paris 7, Paris, 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
Sorin Popa University of California, Los Angeles, Los Angeles, CA
A co-publication of the AMS and Clay Mathematics Institute
Available Formats:
Softcover ISBN: 978-0-8218-5203-3
Product Code: CMIP/11
List Price: $145.00 MAA Member Price:$130.50
AMS Member Price: $116.00 Click above image for expanded view Quanta of Maths Edited by: Etienne Blanchard University of Paris 7, Paris, 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 Sorin Popa University of California, Los Angeles, Los Angeles, CA A co-publication of the AMS and Clay Mathematics Institute Available Formats:  Softcover ISBN: 978-0-8218-5203-3 Product Code: CMIP/11  List Price:$145.00 MAA Member Price: $130.50 AMS Member Price:$116.00
• Book Details

Clay Mathematics Proceedings
Volume: 112010; 675 pp
MSC: Primary 58;

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.

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

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Volume: 112010; 675 pp
MSC: Primary 58;

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.