I am a global analyst. I use operator methods in geometry, particular when they encode geometric/topological information. I typically work with differential operators on vector bundles and analyse them through functional calculus and real-variable harmonic analysis.

My current focus is on index theory in settings with boundary. I have contributed extensively to the topic over the past 5 years, in particular upgrading Fourier circle methods with the holomorphic functional calculus. This has allowed for analysis of non-Dirac-type operators and also non-compact boundary.

Broadly speaking, the following are my detailed interests:

• Global analysis - use of operator methods in geometry, index theory.
• 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.