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Some Noncommutative Spheres
Noncommutative geometry provides us various means to deal with noncommutative phenomena in mathematics, and C*-algebras (and von Neumann algebras)...
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A noncommutative Tauberian theorem and Weyl asymptotics in noncommutative geometry
We prove a Tauberian theorem for singular values of noncommuting operators which allows us to prove exact asymptotic formulas in noncommutative...
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Metric perturbations in noncommutative gravity
We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up...
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Noncommutative Line Bundles and Gerbes
We introduce noncommutative line bundles and gerbes within the framework of deformation quantization. The Seiberg-Witten map is used to construct the...
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Forces from Connes’ Geometry
Einstein derived general relativity from Riemannian geometry. Connes extends this derivation to noncommutative geometry and obtains electro–magnetic,...
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Gauge theory on twist-noncommutative spaces
We construct actions for four dimensional noncommutative Yang-Mills theory with star-gauge symmetry, with non-constant noncommutativity, to all...
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Quasinormal modes in noncommutative Schwarzschild black holes: a spectral analysis
We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both...
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Noncommutative instantons in diverse dimensions
This is a mini-review about generalized instantons of noncommutative gauge theories in dimensions 4, 6 and 8, with emphasis on their realizations in...
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Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry
We compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large N limit. These ensembles are toy models...
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Index Theorems and Noncommutative Topology
These lecture notes are mainly devoted to a K-theory proof of the Atiyah-Singer index theorem. Some applications of the K-theory to noncommutative...
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Lectures on Two-Dimensional Noncommutative Gauge Theory Quantization
These notes are devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with...
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On Multimatrix Models Motivated by Random Noncommutative Geometry II: A Yang-Mills-Higgs Matrix Model
We continue the study of fuzzy geometries inside Connes’ spectral formalism and their relation to multimatrix models. In this companion paper to...
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Morita Equivalence, Picard Groupoids and Noncommutative Field Theories
In this article we review recent developments on Morita equivalence of star products and their Picard groups. We point out the relations between...
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Noncommutative Networks on a Cylinder
In this paper a double quasi Poisson bracket in the sense of Van den Bergh is constructed on the space of noncommutative weights of arcs of a...
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The optical features of noncommutative charged 4D-AdS-Einstein–Gauss–Bonnet black hole: shadow and deflection angle
In this paper, we have explored the optical characteristics, namely the shadow and the deflection angle, inherent to the solution of a...
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Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces
I give an introduction to Euclidean quantum field theory from the point of view of statistical physics, with emphasis both on Feynman graphs and on...
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Noncommutative gauge and gravity theories and geometric Seiberg–Witten map
We give a pedagogical account of noncommutative gauge and gravity theories, where the exterior product between forms is deformed into a
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Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
Some noncommutative (NC) theories posses a certain type of dualities that are implicitly built within their structure. In this paper we establish...
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Noncommutative Spheres and Instantons
We report on some recent work on deformation of spaces, notably deformation of spheres, describing two classes of examples.
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Noncommutative formulation of Schwarzschild black hole and its physical properties
In this paper, we study the effects of noncommutativity on solutions and the thermodynamic properties of a Schwarzschild black hole. Such...
