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.