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Spectral truncations in noncommutative geometry and operator systems
Alain Connes, Walter D. van Suijlekom
In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e. imposing an ultraviolet cutoff in…
Noncommutative Geometry, the spectral standpoint
Alain Connes
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…
On an idea of Michael Atiyah
Alain Connes
In this note we investigate the idea of Michael Atiyah of using, as a possible approach to the Theorem of Feit-Thompson on the solvability of finite groups of odd order, the iterat…
The term a_4 in the heat kernel expansion of noncommutative tori
Alain Connes, Farzad Fathizadeh
We consider the Laplacian associated with a general metric in the canonical conformal structure of the noncommutative two torus, and calculate a local expression for the term a_4 t…
Modular Curvature for Noncommutative Two-Tori
Alain Connes, Henri Moscovici
In this paper we investigate the curvature of conformal deformations by noncommutative Weyl factors of a flat metric on a noncommutative 2-torus, by analyzing in the framework of s…
On the arithmetic of the BC-system
Alain Connes, Caterina Consani
For each prime p and each embedding of the multiplicative group of an algebraic closure of F_p as complex roots of unity, we construct a p-adic indecomposable representation of the…