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

• Submersion constructions for geometries with parallel skew torsion (preprint, 2024), with Andrei Moroianu. arXiv:2409.14421.
• On the rigidity of the complex Grassmannians (preprint, 2024), with Uwe Semmelmann. (This will be made into a joint publication with Stuart J. Hall.) arXiv:2403.04681.
• 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.
• 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.
• 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.
• 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.
• 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.