Research

My research interests include (but are not limited to) Riemannian geometry, curvature, special holonomy, geometric analysis, manifolds with symmetries and Lie theory.

Publication list

1. Formalizing a classification theorem for low-dimensional solvable Lie algebras in Lean (preprint, 2025), with Viviana del Barco, Gustavo Infanti and Exequiel Rivas. arXiv:2505.19975.
2. Sandwich operators and Einstein deformations of compact symmetric spaces related to Jordan algebras (preprint, 2024), with Stuart J. Hall and Uwe Semmelmann. arXiv:2412.08770.
3. Submersion constructions for geometries with parallel skew torsion (preprint, 2024), with Andrei Moroianu. arXiv:2409.14421.
4. On the rigidity of the complex Grassmannians, Trans. AMS, vol. 378, no. 6, pp. 4335-4367 (2025), with Stuart J. Hall and Uwe Semmelmann. DOI 10.1090/tran/9402
5. The Lichnerowicz Laplacian on normal homogeneous spaces, J. Reine Angew. Math. (Crelle’s Journal), vol. 2024, no. 814, pp. 91-115 (2024). DOI 10.1515/crelle-2024-0038.
6. Doctoral thesis: Stability of Einstein metrics on homogeneous spaces (2023). DOI 10.18419/opus-13515. This cumulative dissertation contains my first four articles together with an expository part.
7. Stability of the Non-Symmetric Space ${\mathrm{E}}_7/\mathrm{PSO}(8)$, Adv. Math., vol. 432, no. 109268 (2023), with Uwe Semmelmann and Gregor Weingart. DOI 10.1016/j.aim.2023.109268.
8. Coindex and Rigidity of Einstein Metrics on Homogeneous Gray Manifolds, J. Geom. Anal., vol. 32, no. 302 (2022). DOI 10.1007/s12220-022-01061-4.
9. Stability of Einstein metrics on symmetric spaces of compact type, Ann. Glob. Anal. Geom., vol. 61, pp. 333-357 (2022). DOI 10.1007/s10455-021-09810-4.

Miscellaneous

• A SageMath Jupyter notebook and accompanying LiE files used at a software demo (Lie theory and branching in LiE and SageMath) which I gave at the Problem-Solving Workshop Computational Geometric Analysis at CUNY (2025).
• Grimoire of curvature sign conventions, conditions, operators, and examples (2025, work in progress). A reference to clear up the confusion on signs and factors that may arise when manipulating curvature expressions.
• Minimal Submanifolds in Spheres (2023). Notes for a lecture at a seminar on submanifolds in Stuttgart.
• Spinors, Dirac Operators and Metric Variations (2023). English translation of the 1992 article by Jean-Pierre Bourguignon and Paul Gauduchon.