2026-07-30T13:30:55Zhttps://ce.visuallibrary.net/ubpb/oai/

oai:ce.visuallibrary.net/ubpb:13996702026-07-23T15:00:04Zubpbcebook

vls/2603nrwcece.visuallibrary.netvdCyclic cohomology at 40: achievements and future prospectsVirtual Conference Cyclic Cohomology at 40: achievements and future prospects, September 27 - October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON CanadaVirtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects 2021 OnlineautConnes, Alain1947-HerausgeberVerfasseredtautConsani, Caterina1963-HerausgeberVerfasseredtautDundas, Bjørn Ian1963-HerausgeberVerfasseredtautKhalkhali, Masoud1963-HerausgeberVerfasseredtautMoscovici, Henri1944-HerausgeberVerfasseredtauttextconference publicationTextKonferenzschrift-2021-OnlinexxuXD-USProvidence, Rhode IslandAMS, American Mathematical Society[2023]2023monographicengprintx, 579 Seiten : Illustrationen, Diagrammeohne Hilfsmittel zu benutzenBandThis volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27-October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada.Cyclic cohomology, since its discovery forty years ago in noncommutative differential geometry, has become a fundamental mathematical tool with applications in domains as diverse as analysis, algebraic K-theory, algebraic geometry, arithmetic geometry, solid state physics and quantum field theory.The reader will find survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc., in which cyclic homology plays the role of a unifying theme.The researcher will find frontier research articles in which the cyclic theory provides a computational tool of great relevance. In particular, in analysis cyclic cohomology index formulas capture the higher invariants of manifolds, where the group symmetries are extended to Hopf algebra actions, and where Lie algebra cohomology is greatly extended to the cyclic cohomology of Hopf algebras which becomes the natural receptacle for characteristic classes. In algebraic topology the cyclotomic structure obtained using the cyclic subgroups of the circle action on topological Hochschild homology gives rise to remarkably significant arithmetic structures intimately related to crystalline cohomology through the de Rham-Witt complex, Fontaine's theory and the Fargues-Fontaine curve.A. Connes, C. Consani, B. I. Dundas, M. Khalkhali, H. Moscovici, editorsIncludes bibliographical referencesHomology theoryCongressesAlgebraic cyclesCongressesNoncommutative differential geometryCongressesNumber theory -- Zeta and $L$-functions: analytic theory -- Relations with noncommutative geometryAlgebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic varieties and schemes; Arakelov theory; heightsAssociative rings and algebras -- Homological methods -- (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Hopf algebras and their applicationsAssociative rings and algebras -- Hopf algebras, quantum groups and related topics -- Bialgebras$K$-theory -- Higher algebraic $K$-theory -- $K$-theory and homology; cyclic homology and cohomologyFunctional analysis -- Selfadjoint operator algebras ($C^*$-algebras, von Neumann ($W^*$-) algebras, etc.) -- Noncommutative differential geometryGlobal analysis, analysis on manifolds -- Infinite-dimensional manifolds -- Noncommutative geometry (à la Connes)Quantum theory -- Quantum field theory; related classical field theories -- Noncommutative geometry methodsQuantum theory -- Groups and algebras in quantum theory -- Noncommutative geometryQA612.3514/.2311M55 14G40 16E40 16T05 16T10 19D55 46L87 58B34 81T75 81R609781470469771137558411099372482570706441HT030022523Online-Ausgabe9781470472634Proceedings of symposia in pure mathematicsvolume 105(DE-605)HT00123505049HBZ_BIE49HBZ_WUP49HBZ_PAD49HBZ_ULB49HBZ_FUHrda23053020260720080233.02609489ger https://ce.visuallibrary.net//domainresource/static/graphics/connectors/viewerLogo.gif http://193.30.112.129:83/F/?func=find-c&ccl_term=ICS%3D2609489 https://ce.visuallibrary.net/id/1399670 https://ce.visuallibrary.net/i3f/v20/1399670/manifest https://ce.visuallibrary.net/proto_ftsearch/1399670