I am generally interested in the analysis of operators on sub-riemannian manifolds (particularly those manifolds which appear as the configuration space of mechanical systems) using representation theory. Some general research dierctions include:
Semi-classical analysis of hypoelliptic operators:
- Developing a robust symbol calculus on sub-Riemannian manifolds using representation theory.
- Computing quantum limits for subelliptic operators on sub-Riemannian manifolds.
Integral geometry and X-ray transforms on Carnot Groups:
- Proving injectivity and stability of X-ray transforms in the “flat” sub-Riemannian case””.
- Adapding results locally to general sub-riemannian manifolds.