5 papers
Noncommutative Laplacian and numerical approximation of Laplace-Beltrami spectrum of compact Riemann surfaces
Damien Tageddine, Jean-Christophe Nave
We derive a numerical approximation of the Laplace-Beltrami operator on compact surfaces embedded in with an axial symmetry. To do so we use a noncommutative Laplace…
Noncommutative geometry on the Berkovich projective line
Masoud Khalkhali, Damien Tageddine
We construct several -algebras and spectral triples associated to the Berkovich projective line . In the commutative setting, we…
Structure preserving discretization: A Berezin-Toeplitz Quantization viewpoint
Damien Tageddine, Jean-Christophe Nave
In this paper, we introduce a comprehensive axiomatization of structure-preserving discretization through the framework of commutative diagrams. By establishing a formal language t…
Statistical Fluctuation of Infinitesimal Spaces
Damien Tageddine, Jean-Christophe Nave
This paper is a follow-up on the \emph{noncommutative differential geometry on infinitesimal spaces} [15]. In the present work, we extend the algebraic convergence from [15] to the…
Noncommutative Differential Geometry on Infinitesimal Spaces
Damien Tageddine, Jean-Christophe Nave
In this paper, we use the language of noncommutative differential geometry to formalise discrete differential calculus. We begin with a brief review of inverse limit of posets as a…