Title: Hypoellipticity, pseudodifferential calculi and groupoids
Abstract: A differential operator P is hypoelliptic if it has the smoothness of solutions property: roughly, if Pf=g with g smooth then f is smooth. The best-known examples are elliptic operators, like the Laplacian, but there are many others, such as the heat operator, the Kolmogorov operator, or Hörmander’s sums-of-squares operators.
In the late 70s, it was realized that hypoellipticity is linked to the representation theory of nilpotent Lie groups (Rockland, Beals-Greiner, Helffer-Nourrigat,...). Helffer and Nourrigat made a broad conjecture encompassing most of the known examples. We will recount this story and show how the Helffer-Nourrigat conjecture can be solved using ideas on the tangent groupoid from Connes and Debord-Skandalis.
If you are interested in participating online please contact Tobias Weich or Benjamin Delarue in order to receive the login details.