Quanta of Maths

The work of Alain Connes has cut a wide swath across several areas of math- ematics 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 II₁ 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 teh 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 F₁, quantum modular forms;
• differential K-theory, cyclic theory and S-cohomology.

Authors: Paul Baum, Dietmar Bisch, Étienne Blanchard, Simon Brain, Dan Burghelea, Pierre Cartier, Ali Chamseddine, Joachim Cuntz, Paramita Das, Michel Dubois-Violette, Alice Guionnet, Nigel Higson, V. F. R. Jones, Max Karoubi, Masoud Khalkhali, Dirk Kreimer, Shamindra Kumar Ghosh, Vincent Lafforgue, Giovanni Landi, J.-L. Loday, Xin Li, Yuri Manin, Matilde Marcolli, Florian Martin, Henri Moscovici, Alejandro Perez, Sorin Popa, Marc Rieffel, M. Ronco, Carlo Rovelli, Thomas Schick, D. Shyyakhtenko, James Simons, Erling Størmer, Dennie Sullivan, Stefaan Vaes, Alain Valette, Raimar Wulkenhaar, Guoliang Yu, Don Zagier

Available at the AMS bookstore