I'm primarily interested in the interactions between harmonic analysis
and geometry, and in particular using harmonic analysis to analyse
low-regularity situations on manifolds and also vector bundles.
Currently, I'm interested in boundary value problems for
first-order operators on bundles, using the language of (bi)-sectorial
- Harmonic analysis - in the flavour of Calderon, Zygmund, Stein, etc.
- Geometric analysis - analysis on non-compact manifolds, non-smooth metrics, analysis on measure metric spaces, Spin geometry.
- Boundary value problems - first-order boundary value problems on bundles, non-smooth coefficients, non-compact boundary.
- Spectral and operator theory - essential self-adjointness, asymptotics of eigenvalues, etc.