Pseudodifferential operators on noncommutative tori: a survey

Pseudodifferential and Fourier integral operators on manifolds (58J40) Deformation quantization, star products (53D55) Noncommutative geometry (à la Connes) (58B34) Pseudodifferential operators (47G30)

Cites Work

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Modular curvature and Morita equivalence
Classification of spin structures on the noncommutative \(n\)-torus
The Gauss-Bonnet theorem for noncommutative two tori with a general conformal structure
A canonical trace associated with certain spectral triples
Noncommutative residue and canonical trace on noncommutative tori. Uniqueness results
Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
Deformation quantization using groupoids. The case of toric manifolds
Wave equations on Lorentzian manifolds and quantization.
C*-algebras associated with irrational rotations
Modular curvature for toric noncommutative manifolds
The local index formula in noncommutative geometry
Local index formulae on noncommutative orbifolds and equivariant zeta functions for the affine metaplectic group
Noncommutative geometry and particle physics
Spin geometry of the rational noncommutative torus
A groupoid approach to pseudodifferential calculi
Scalar curvature for the noncommutative two torus
Spectral action on noncommutative torus
Moduli spaces of instantons on toric noncommutative manifolds
The canonical trace and the noncommutative residue on the noncommutative torus
The Gauss-Bonnet theorem for the noncommutative two torus
Modular curvature for noncommutative two-tori
Connes-Landi spheres are homogeneous spaces
Modular Gaussian curvature
Traces of Holomorphic Families of Operators on the Noncommutative Torus and on Hilbert Modules
Pseudo-Differential Operators and Symmetries
Deformation quantization for actions of 𝑅^{𝑑}
Spectral Action in Noncommutative Geometry
Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals
Pseudodifferential calculus on noncommutative tori, II. Main properties
Noncommutative manifolds, the instanton algebra and isospectral deformations

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