Research Interests
Non-smooth Differential Geometry
- Low regularity Lorentzian geometry
- Synthetic Lorentzian geometry, Lorentzian length spaces
- Comparison geometry
- Optimal Transport
- Distributional geometry
General Relativity
- Low regularity spacetimes
- Singularity theorems
- Synthetic methods
Nonlinear Functional Analysis, Algebras of Generalized Functions
- Colombeau Algebras
- Diffeomorphism invariant theories of nonlinear generalized functions
- Applications to differential geometry
- Applications to General Relativity
- Generalized smooth functions
Symmetry Groups of Differential Equations
- Group Analysis for Generalized Functions
- Classical Group Analysis
- Classification problems
Partial Differential Equations
- Singular non-linear problems
- Parabolic equations on Riemannian manifolds