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 operators. Also:
  • 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.