The seminar presented recent advances in the spectral theory of hypoelliptic operators on compact manifolds.

The hypoellipticity of the differential operator guarantees that any distributional solution is actually smooth on the region where the coefficients are smooth.

The research seminar focused on how a hypoelliptic operator affects the regularity of solutions to partial differential equations.

To analyze the smoothing effects, the seminar focused on hypoelliptic operators arising in sub-Riemannian geometry.