The main focus of my research is on spectral analysis of filtered manifolds.
More specifically, I am studying the analytic torsion of the Rumin complex for generic rank two distributions in dimension five, a.k.a. (2,3,5) distributions.
Presently, I am applying methods form parabolic geometry to compute local quantities appearing in the small time asymptotic expansion of heat kernels associated with the Rumin complex, and I am using harmonic analysis on nilpotent Lie groups to relate the whole analytic torsion function of the Rumin complex on nilmanifolds to number theoretic properties of the corresponding lattice.
I am also working on infinite dimensional groups of diffeomorphisms and their coadjoint orbits.
https://orcid.org/0000-0002-7064-2215