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. 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.
2. Submersion constructions for geometries with parallel skew torsion (preprint, 2024), with Andrei Moroianu. arXiv:2409.14421.
3. On the rigidity of the complex Grassmannians, to appear in Trans. AMS, with Stuart J. Hall and Uwe Semmelmann. Preprint version: arXiv:2403.04681.
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.
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

• Grimoire of curvature sign conventions, conditions, operators, and examples (2024, 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.