کوانتاي رياضيات: کنفرانس به افتخار آلن کونز: هندسه غیرمتقارن

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) A Geometric Description Of Equivariant K-homology For Proper Actions / Paul Baum, Nigel Higson And Thomas Schick -- The Planar Algebra Of Diagonal Subfactors / Dietmar Bisch, Paramita Das And Shamindra Kumar Ghosh -- K1-injectivity For Properly Infinite C*-algebras / Étienne Blanchard -- Families Of Monads And Instantons From A Noncommutative Adhm Construction / Simon Brain And Giovanni Landi -- Cyclic Theory For Commutative Differential Graded Algebras And S-cohomology / Dan Burghelea -- Vinberg Algebras, Lie Groups And Combinatorics / Pierre Cartier -- Noncommutative Geometry As The Key To Unlock The Secrets Of Space-time / Ali H. Chamseddine -- The Regular C*-algebra Of An Integral Domain / Joachim Cuntz And Xin Liu -- Noncommutative Coordinate Algebras / Michel Dubois-violette -- Random Matrices, Free Probability, Planar Algebras And Subfactors / A. Guionnet, V.f.r. Jones, D. Shlyakhtenko -- The Tangent Groupoid And The Index Theorem / Nigel Higson -- Le Théorème De Périodicité En K.-théorie Hermitienne / Max Karoubi - A Short Survey Of Cyclic Cohomology / Masoud Khalkhali -- The Core Hopf Algebra / Dirk Kreimer -- Propriété Renforcées Et Conjecture De Baum-connes / Vincent Lafforgue -- Combinatorial Hopf Algebras / J.-l. Loday And M. Ronco -- Cyclotomy And Analytical Geometry Over F1 / Yuri I. Manin -- Motivic Renormalization And Singularities / Matilde Marcolli -- Free Groups And Reduced 1-cohomology Of Unitary Representations / Florian Martin And Alain Valette -- Local Index Formula And Twisted Spectral Triples / Henri Moscovici -- Observables In Quantum Gravity / Alejandro Perez And Carlo Rovelli -- On The Fundamental Group Of Ii1 Factors And Equivalence Relations Arising From Group Actions / Sorin Popa And Stefaan Vaes -- Leibniz Seminorms For Matrix Algebras Converge To The Sphere / Marc A. Rieffel -- Structured Vector Bundles Define Differential K-theory / James Simons And Dennis Sullivan -- Entropy In Operator Algebras / Erling Størmer -- Non-compact Spectral Triples With Finite Volume / Raimar Wulkenhaar -- A Characterization Of The Image Of The Baum-connes Map / Guoliang Yu -- Quantum Modular Forms / Don Zagier. Etienne Blanchard ... [et Al.], Editors. Includes Bibliographical References.