Softcover ISBN:  9780821852033 
Product Code:  CMIP/11 
List Price:  $145.00 
MAA Member Price:  $130.50 
AMS Member Price:  $116.00 

Book DetailsClay Mathematics ProceedingsVolume: 11; 2010; 675 ppMSC: 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 1cohomology, Leibniz seminorms and quantum metric spaces;
 von Neumann algebras, fundamental Group of \(\mathrm{II}_1\) factors, subfactors and planar algebras;
 BaumConnes conjecture and property T, equivariant Khomology, Hermitian Ktheory;
 cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem;
 noncommutative geometry and spacetime, spectral action principle, quantum gravity, noncommutative ADHM and instantons, noncompact 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 Ktheory, cyclic theory and Scohomology.
ReadershipGraduate students and research mathematicians interested in recent developments in various areas of mathematics.

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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 1cohomology, Leibniz seminorms and quantum metric spaces;
 von Neumann algebras, fundamental Group of \(\mathrm{II}_1\) factors, subfactors and planar algebras;
 BaumConnes conjecture and property T, equivariant Khomology, Hermitian Ktheory;
 cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem;
 noncommutative geometry and spacetime, spectral action principle, quantum gravity, noncommutative ADHM and instantons, noncompact 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 Ktheory, cyclic theory and Scohomology.
Graduate students and research mathematicians interested in recent developments in various areas of mathematics.