Dr. Gaston Nieuviarts

About me

I am a mathematical physicist working on noncommutative geometry and its applications to fundamental physics. I completed my PhD at the Centre de Physique Théorique (CPT), Aix-Marseille Université, in 2022, and subsequently conducted postdoctoral research at the Department of Mathematics (DIMA), University of Genoa.

My research spans noncommutative gauge theories, AF algebras, spectral triples and spectral actions, twisted spectral geometry, torsion, and pseudo-Riemannian structures. A central focus of my recent work is the metric signature problem, particularly the emergence of Lorentzian structures within twisted and almost-commutative spectral frameworks.

Alongside this research, I lead the scientific and technical design of artificial intelligence tools for education within a deeptech  startup project I co-founded with Bastien Marguet, currently incubated at PULSALYS.

More information can be found in my Curriculum Vitae or in my LinkedIn page.

E-mail : gaston[dot]nieuviarts[dot]wk[at]gmail[dot]com

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.

Selected Scientific Activities

International Conference at CIRM, Marseille (7 to 11 April 2025) :

Applications of NonCommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time.

Building on a proposal I made during my PhD, the conference was subsequently developed through a collective scientific effort. I served as a member of its Organizing Committee and also contributed to the scientific programme as a speaker.

Doctoral Research and Scientific Guidance :

Together with Thierry Masson, I contribute to the scientific guidance of an ongoing PhD project extending the research direction on metric signature change that I initiated during my postdoctoral work at the University of Genoa.

Published Articles and Preprints

G. N (2026): Emergence of Time from a Twisted Spectral Triple in Almost-Commutative Geometry

Accepted in J. Noncommut. Geom. 

Preprint: arXiv:2512.15450

G. N (2026): Emergence of Lorentz symmetry from an almost-commutative twisted spectral triple

Published in Int. J. Geom. Methods Mod. Phys.

Preprint: arXiv:2502.18105

G. N  (2025): Signature change by a morphism of spectral triples

Published in 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.

arXiv:2401.07848

G. N  (2023): Noncommutative Geometry and Gauge theories on AF algebras (PhD thesis)

arXiv:2304.08505

T. Masson, G. N (2023): Lifting Bratteli Diagrams between Krajewski Diagrams: Spectral Triples, Spectral Actions, and AF algebras

Published in J. Geom. Phys. Vol. 187, p. 104784

arXiv:2207.04466 

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

arXiv:2106.08358