Research

My research lies in differential geometry, with a particular focus on spectral geometry, homogeneous spaces, and computational questions arising from geometric problems.

In my dissertation, I investigate explicit spectral questions for Laplace operators on homogeneous spaces and related principal fiber bundles. Beyond classical analytical methods, a major driver of my work is the application of modern technology to theoretical problems: I leverage symbolic computation (Python, SageMath) to tackle complex geometric calculations, and I actively explore the integration of AI tools into mathematical research. Currently, I am particularly fascinated by the use of physics-informed neural networks to discover new geometric objects.

Blackboard covered with notes and formulas in differential geometry — Discussing the Laplacian at the National University of Córdoba, Argentina.

Publications

2026. Explicit Laplace Spectra of Homogeneous Principal Bundles. Ilka Agricola, Leandro Cagliero, Jonas Henkel. arXiv:2605.11177v1 [math.DG]. Submitted to Journal of Geometric Analysis.
2026. Hodge Laplacian on 1-forms of homogeneous 3-spheres. Jonas Henkel, Emilio Lauret. arXiv:2605.05406 [math.DG]. Submitted to Communications in Analysis and Geometry.
2026. A Machine Learning Approach to the Nirenberg Problem. Cortes, Esteban-Casadevall, Feng, Henkel, Hirst, Schettini-Gherardini, Stapleton. arXiv:2602.12368 [cs.LG]. Submitted to Journal of the London Mathematical Society.
2025. The Laplace-Beltrami Spectrum on Naturally Reductive Homogeneous Spaces. Ilka Agricola, Jonas Henkel. arXiv:2503.21416 [math.DG]. Submitted to Mathematische Zeitschrift.
2025. The Mathematician's Assistant: Integrating AI into Research Practice. Jonas Henkel. Mathematische Semesterberichte, 72, 117-144. doi:10.1007/s00591-025-00400-0.