Quanta of Maths
Étienne 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)
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.