Cyclic cohomology at 40 : achievements and future prospects / A. Connes, C. Consani, B.I. Dundas, M. Khalkhali, and H. Moscovici, editors.

• Preface -- Chern-Connes-Karoubi character ismorphisms and algebras of symbols pseudodifferential operators / A. Baldare, M. Benameur, and V. Nistor -- One Perrot's index cocycles / J. Block, H. Higson, and J. Sanchez Jr. -- The Chern-Baum-Connes assembly map for Lie groupoids / P. Carrillo Rouse -- Hochschild homology, trace map 9-cycles / A. Connes and C. Consani -- Cyclic theory and the pericyclic category / A. Connes and C. Consani -- The image of Bott periodicity in cyclic homology / J. Cuntz -- Applications of topological cycle homology to algebraic K-theory / B. I. Dundas -- Algebraic K-theory and generalized stable homotopy theory / D. Gepner -- Cyclic cohomology and the extended Heisenberg calculus of Epstein and Melrose / A. Gorokhovsky and E. Van Erp -- Topological cyclic homology and the Fargues-Fontaine curve / L. Hesselholt -- Hopf cyclic cohomology and beyond / M. Khalkhali and I. Shapiro -- The Hochschild cohomology of uniform Roe algebras / M. Lorentz -- Quantum differentiabiltiy : the analytical perspective / E. McDonald, F. Sukochev, and X. Xiong -- Local cyclic homology for nonarchimedean Banach algebras / R. Meyer and D. Mukherjee -- On the van Est analogy in Hopf cyclic cohomology / H. Moscovici -- Primary and secondary invariants of Dirac operators on G-proper manifolds / P. Piazza and X. Tang -- Localization in Hochschild homology / M. J. Pflaum -- Cyclic homology and group actions / R. Ponge -- Cyclic cocycles and quantized pairings in materials science / E. Prodan -- Periodic cyclic homology of crossed products / M. Puschnigg -- Trace expansions and equivariant trances on an algebra of Fourier integral operators on Rn / A. Savin and E. Schrohe -- Cartan motion group and orbital integrals / Y. Song and X. Tang -- On noncommutative crystalline cohomology / B. Tsygan -- Cyclic cocycles and one-loop corrections in the spectral action / T. D. H. Nuland and and W. D. Van Suijlekom -- l1-higher index, l1-higher rho invariant and cyclic cohomology / J. Wang, Z. Xie, and G. Yu.

• "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.."-- 

Ämnesord

Quantum theory.  (LCSH)

Homology theory  -- Congresses. (LCSH)

Algebraic cycles  -- Congresses. (LCSH)

Noncommutative differential geometry  -- Congresses. (LCSH)

Cohomology operations  -- Congresses. (LCSH)

K-theory  -- Congresses. (LCSH)

Quantum Theory  (MeSH)

Algebraic cycles.  (fast)

Cohomology operations.  (fast)

Homology theory.  (fast)

K-theory.  (fast)

Noncommutative differential geometry.  (fast)

Quantum theory.  (fast)

Genre

Congress  (MeSH)

proceedings (reports)  (aat)

Conference papers and proceedings.  (fast)

Conference papers and proceedings.  (lcgft)

Klassifikation

QA612.33 (LCC)

514/.23 (DDC)

11M55 (msc)

Tepb (kssb/8 (machine generated))