Jonas Henkel

Research

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

My dissertation project concerns explicit spectral questions for Laplace operators on homogeneous spaces and related principal fiber bundles. Alongside this, I use symbolic computation with Python and SageMath to support calculations in differential geometry, and I am interested in how AI-based methods, including machine learning and neural-network-based approaches, can support mathematical research.

Blackboard covered with notes and formulas in differential geometry

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.