- Global analysis
I work on analysis of elliptic/hypoelliptic operators arising from geometries. In particular I am interested in the construction of hypoelliptic operators on filtered manifolds as well as spectral invariances of such operators.
I have also studied algebras of pseudodifferential operators and noncommutative geometric invariants of them.
- Differential geometry and topology
Global aspects of geometry of filtered manifolds such as contact manifolds and Cartan/parabolic geometries.
I have also worked on regularity and microlocal properties of distributions and generalized functions.