Research

My research interests include Riemannian geometry (curvature, special holonomy, spectral geometry), \(G\)-structures (with torsion), geometric analysis, manifolds with symmetries, Lie theory, and formalization of mathematics.

Preprints

1. The Standard Model Gauge Group from the Exceptional Jordan Algebra (2026), with John C. Baez. arXiv:2606.15235.
2. Geometries with parallel, skew-symmetric and closed torsion (2026), with Andrei Moroianu. arXiv:2605.13227.
3. Balanced subsets in root systems (2026), with Andrei Moroianu. arXiv:2605.11219.
4. Einstein metrics, their moduli spaces and stability (survey, 2025), with Uwe Semmelmann. arXiv:2507.18463.
5. Sandwich operators and Einstein deformations of compact symmetric spaces related to Jordan algebras (2024), with Stuart J. Hall and Uwe Semmelmann. arXiv:2412.08770.

Peer-reviewed publications

1. Submersion constructions for geometries with parallel skew torsion, J. Geom. Anal., vol. 36, no. 389 (2026), with Andrei Moroianu. DOI 10.1007/s12220-026-02627-2.
2. Formalizing a Classification Theorem for Low-Dimensional Solvable Lie Algebras in Lean (2025), with Viviana del Barco, Gustavo Infanti and Exequiel Rivas. In: V. de Paiva, P. Koepke (eds.), Intelligent Computer Mathematics. CICM 2025. Lecture Notes in Artificial Intelligence, vol. 16136, Springer. DOI 10.1007/978-3-032-07021-0_18.
3. 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.
4. 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.   –> CORRIGENDUM <–
5. 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.
6. 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.
7. 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.
8. 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

• Ongoing formalization project (in Lean) on the foundations of synthetic incidence geometry, focusing on affine and projective spaces, in particular finite ones.
• BRIDGES lectures \(G_2\) in action, and a mathematical theory of exceptions (2025). Lecture notes for a summer school course by Laurent Manivel at the BRIDGES meeting 2024 in Cargèse which Vladimiro Benedetti, Gaia Comaschi, Alan Muniz, and I helped write.
• 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.
• Spinors, Dirac Operators and Metric Variations (2023). English translation of the 1992 article by Jean-Pierre Bourguignon and Paul Gauduchon.