Armin van de Venn

Beyond Riemannian Geometry in Fundamental Physics

My research lies at the intersection of gravitation, geometry, and quantum theory. It explores extended geometric foundations of spacetime and their profound implications for our understanding of the universe.

Metric-Affine Gravity

My main interest focuses on metric–affine gravity, where the spacetime connection is treated as an independent geometric object, allowing for torsion and nonmetricity. I investigate the physical consequences of these generalized geometries in cosmology and gravitation, including singularity theorems, cosmological dynamics, and possible geometric explanations for dark energy and related phenomena.

Geometric Foundations of Gauge Theories

I am especially interested the mathematical structure of gravitational theories, but more broadly the geometry of gauge theories. I study gauge theories from the perspective of fibre bundles and connections, interpreting metric–affine gravity as a gauge theory of spacetime symmetries. This includes work on connections, curvature, torsion, and nonmetricity, and their role in both classical and quantum formulations of gravity.

Stochastic Quantisation

In collaboration with Prof. Tomoi Koide, I have investigated stochastic quantisation in curved and generalized geometric settings, incorporating torsion and nonmetricity beyond the Riemannian framework. We showed that spacetime torsion can induce nonlinear corrections to the Schrödinger equation, even for spinless quantum systems.

Information Geometry

Together with Prof. Tomoi Koide, I have also explored information geometry as a framework linking statistical physics, stochastic processes, and gravitational geometry. In this setting, nonmetricity arises naturally as a geometric feature of statistical manifolds. We showed that canonically constrained Brownian bridges can be described as geodesics on a statistical manifold, providing a concrete physical realization of information-geometric structures and highlighting their potential relevance for fundamental physics.

New Horizons for Physics

My research demonstrates how extending the geometric foundations of spacetime can lead to genuinely new physical effects, rather than constituting a merely formal generalization of general relativity. By treating the spacetime connection as an independent geometric object within metric–affine gravity, new degrees of freedom such as torsion and nonmetricity emerge, which can have observable consequences in cosmology, quantum theory, and gravitational dynamics. A central message is that geometry itself can act as a source of physical phenomena, influencing dynamics even in regimes where standard curvature-based effects would be absent. As such, advanced geometry is not an abstract layer added to physics, but a powerful and practical language that reveals deep connections between seemingly distinct areas of theoretical physics.

Future Directions

A central direction of my current research is the systematic development of metric–affine gravity as a framework that is both mathematically well-founded and physically predictive. An important open question is how torsion and nonmetricity can be consistently incorporated into cosmological and gravitational models in a way that leads to testable effects.

I am furthermore interested in strengthening the connection between modern differential geometry and gravity, especially by treating metric–affine gravity explicitly as a gauge theory. This includes exploring the role of fiber bundles, connections, and moduli spaces of geometric structures, and understanding how these mathematical tools help clarify the space of viable gravitational theories.

In collaboration with Prof. Tomoi Koide, I am continuing to investigate stochastic quantisation in generalized geometric settings, with the aim of understanding how spacetime geometry can influence quantum dynamics beyond standard curvature-based effects. A key open problem is to determine whether such geometry-induced quantum corrections could leave new insights into the foundations of quantum mechanics in curved spacetime.

Additionally, I am working with Prof. María José Guzmán on the development of the 3+1 (ADM) formalism within metric–affine gravity. This line of research aims to establish a consistent canonical and dynamical formulation of generalized gravitational theories, with potential applications to numerical relativity and the study of dynamical spacetimes beyond the Riemannian framework.

Overall, I am keen to pursue interdisciplinary collaborations at the interface of gravity, geometry, and quantum theory, and to develop these ideas into a coherent and physically testable research program.

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