Research
My research focuses on Geometric Analysis, where one employs techniques from nonlinear elliptic and parabolic PDEs to answer questions in geometry and topology, often motivated by physics. Some of the topics I am interested in are:
- Geometric flows such as Ricci flow or Mean curvature flow.
- Geometric variational problems: minimal surfaces, spectral geometry, the Yamabe problem and Yang–Mills connections.
- General Relativity: scalar curvature, positive energy theorems and asymptotic foliations.
Publications and preprints
- Regularity of conformal structures on closed 3-manifolds (joint with Rodrigo Avalos and Albachiara Cogo) - arXiv
- Conformal Green functions and Yamabe metrics of Sobolev regularity (joint with Rodrigo Avalos and Albachiara Cogo) - arXiv
- Ancient Solutions to Ricci Flow with Type I curvature growth (joint with Stephen Lynch) - J. Geom. Anal. vol. 34, 119 (2024)
Selected talks
- British Isles Graduate Workshop VI: Minimal Surfaces (Isle of Wight, 2025): “Classification of genus zero shrinkers”
- Geometric Analysis, Differential Geometry and Relativity research seminar (Tübingen, 2025): “Singularity formation in coupled Ricci and Yang–Mills flow”
- Geometry and Topology seminar (Madison, 2025): “Sobolev conformal structures on closed 3-manifolds”
- Geometric Analysis, Differential Geometry and Relativity research seminar (Tübingen, 2024): “Sobolev conformal structures on closed 3-manifolds”
- Mathematical physics colloquium (Tübingen, 2023): “Optimal geometry via parabolic equations”
- Stochastic and Geometric Analysis group seminar (HCM Bonn, 2023): “Ancient Solutions of Ricci flow with Type I curvature growth”
- Geometric Analysis, Differential Geometry and Relativity research seminar (Tübingen, 2022): “Ancient Solutions of Ricci flow with Type I curvature growth”