Cyclic cohomology at 40: achievements and future prospects: virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada
This 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 fo...
Gespeichert in:
| Körperschaft: | |
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| Weitere Verfasser: | , , , , |
| Format: | Tagungsbericht Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2023]
|
| Schriftenreihe: | Proceedings of symposia in pure mathematics
volume 105 |
| Schlagworte: | |
| Zusammenfassung: | This 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. |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | x, 579 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470469771 |
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| spelling | Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects 2021 Online Verfasser (DE-588)1290648883 aut Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada A. Connes, C. Consani, B. I. Dundas, M. Khalkhali, H. Moscovici, editors Providence, Rhode Island American Mathematical Society [2023] x, 579 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Proceedings of symposia in pure mathematics volume 105 Includes bibliographical references This 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. (DE-588)1071861417 Konferenzschrift gnd-content Connes, Alain 1947- (DE-588)112614760 edt Consani, Caterina 1963- (DE-588)131567977 edt Dundas, Bjørn Ian 1963- (DE-588)1034375113 edt Khalkhali, Masoud 1963- (DE-588)136619029 edt Moscovici, Henri 1944- (DE-588)1017369615 edt Erscheint auch als Online-Ausgabe 978-1-470-47263-4 Proceedings of symposia in pure mathematics volume 105 (DE-604)BV000012972 105 |
| spellingShingle | Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada Proceedings of symposia in pure mathematics |
| subject_GND | (DE-588)1071861417 |
| title | Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada |
| title_auth | Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada |
| title_exact_search | Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada |
| title_exact_search_txtP | Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada |
| title_full | Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada A. Connes, C. Consani, B. I. Dundas, M. Khalkhali, H. Moscovici, editors |
| title_fullStr | Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada A. Connes, C. Consani, B. I. Dundas, M. Khalkhali, H. Moscovici, editors |
| title_full_unstemmed | Cyclic cohomology at 40: achievements and future prospects virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada A. Connes, C. Consani, B. I. Dundas, M. Khalkhali, H. Moscovici, editors |
| title_short | Cyclic cohomology at 40: achievements and future prospects |
| title_sort | cyclic cohomology at 40 achievements and future prospects virtual conference cyclic cohomology at 40 achievemants and future prospects september 27 october 1 2021 fields institute for research in mathematical sciences toronto on canada |
| title_sub | virtual Conference "Cyclic Cohomology at 40 : achievemants and future prospects", September 27-October 1, 2021, Fields Institute for Research in Mathematical Sciences Toronto, ON Canada |
| topic_facet | Konferenzschrift |
| volume_link | (DE-604)BV000012972 |
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