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Noncommutative Geometry, the spectral standpoint
[article]
2019
arXiv
pre-print
We report on the following highlights from among the many discoveries made in Noncommutative Geometry since year 2000: 1) The interplay of the geometry with the modular theory for noncommutative tori, 2) Advances on the Baum-Connes conjecture, on coarse geometry and on higher index theory, 3) The geometrization of the pseudo-differential calculi using smooth groupoids, 4) The development of Hopf cyclic cohomology, 5) The increasing role of topological cyclic homology in number theory, and of
arXiv:1910.10407v1
fatcat:25i5d7urbjey3gjfx7r2tonccy