Research
Broadly speaking, my research focuses on Differential Geometry, Partial Differential Equations and Mathematical Physic. More precisely, I employ techniques from nonlinear elliptic and parabolic PDEs to answer questions in geometry, often times 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 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”