On maximally hypoelliptic differential operators.

par Omar Mohsen (Paris-Saclay)

mardi 13 janv. 2026, 14:00 → 15:00 Europe/Paris

Fokko (ICJ)

The class of maximally hypoelliptic differential operators is a large class of differential operators which contains elliptic operators as well as Hörmander’s sum of squares. I will present our work where we define a principal symbol generalising the classical principal symbol for elliptic operators which should be thought of as the analogue of the principal

symbol in sub-Riemannian geometry. Our main theorem is that maximal hypoellipticity is equivalent to invertibility of our principal symbol, thus generalising the main regularity theorem for elliptic operators and confirming a conjecture of Helffer and Nourrigat.  Our proof differs from the proof of the elliptic regularity theorem in its essential use of C* algebras. I will try in the end to explain the role of C* algebras in this theory.