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About me
About me
I did my PhD at the Theoretical Physics Center in Marseille (CPT) and a postdoc at the Mathematics Department in Genoa (DIMA).
I am mainly active in fields related to the application of noncommutative geometry to theoretical physics, in particular concerning
-Noncommutative and pseudo-Riemannian geometries.
-Noncommutative Standard Model, Grand Unified Theories and approximately finite algebras.
-Twisted spectral triples and torsion.
More information can be found in my Curriculum Vitae.
E-mail : gaston[dot]nieuviarts[dot]wk[at]gmail[dot]com
Research Interests
Research Interests
Modern physics describes fundamental interactions through two distinct languages: the curved geometry of General Relativity and the gauge-theoretic framework of Yang–Mills theories. Noncommutative Geometry (NCG) offers a unified alternative, reformulating Riemannian spin geometry through Connes’ spectral triples. In this framework, "almost-commutative" geometries permit to recover the Standard Model and the Higgs sector as purely geometric consequences of a spectral action.
Despite its elegance, this construction is fundamentally Euclidean. To describe realistic physics, one must incorporate causality and Lorentzian signature directly into the algebraic structure. My research operates at this critical interface between NCG, gauge theory, and Lorentzian geometry.
During my PhD, I investigated gauge theories on AF algebras (approximately finite-dimensional). This work connects NCG to the structural challenges of Grand Unified Theories.
More recently, I have focused on the Lorentzian signature problem, addressing the conceptual gap between the Euclidean axioms of spectral triples and the pseudo-Riemannian nature of physical spacetime. By investigating twisted spectral triples and their relation to pseudo-Riemannian structures via a specific notion of morphism, I have developed a framework where the transition between signatures is an inherent consequence of the spectral triple structure. My work demonstrates that the finite noncommutative algebra encoding the Standard Model’s internal symmetries interacts with the manifold to "force" the emergence of a Lorentzian Dirac operator. Within this setting, Lorentzian signatures emerge from the algebraic "entanglement" between the manifold and the internal geometry, providing an alternative to Wick rotations.
My long-term goal is to establish a robust Lorentzian formulation for the noncommutative Standard Model and to demonstrate how geometry, internal symmetries, and time emerge as different facets of a single, unified algebraic–spectral structure.
Published Articles and Preprints
Published Articles and Preprints
G. N (2025): Emergence of Time from a Twisted Spectral Triple in Almost-Commutative Geometry
Submitted to J. Noncommut. Geom.
Preprint: arXiv:2512.15450
G. N (2025): Emergence of Lorentz symmetry from an almost-commutative twisted spectral triple
Submitted to Int. J. Geom. Methods Mod. Phys.
Preprint: arXiv:2502.18105
G. N (2024): Signature change by a morphism of spectral triples
Submitted to J. Geom. Phys.
Preprint: arXiv:2402.05839
P. Martinetti, G. N, R. Zeitoun (2024): Torsion and Lorentz symmetry from Twisted Spectral Triples
Submitted to J. Math. Phys. Anal. Geom.
G. N (2023): Noncommutative Geometry and Gauge theories on AF algebras (PhD thesis)
T. Masson, G. N (2022): Lifting Bratteli Diagrams between Krajewski Diagrams: Spectral Triples, Spectral Actions, and AF algebras
Published in J. Geom. Phys. Vol. 187, p. 104784
T. Masson, G. N (2021): Derivation-based Noncommutative Field Theories on AF algebras
Published in Int. J. Geom. Methods Mod. Phys. Vol. 18, No. 13, 2150213
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