Research Interest

  • 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.