Speaker
Description
In 1979, Helffer and Nourrigat made a very broad conjecture about the hypoellipticity of differential operators which are polynomials in a family of vector fields. Their conjecture generalises a vast number of results — eg, the elliptic regularity theorem, Hörmander’s sums-of- squares theorem, and Rockland’s Theorem (proven by Helffer-Nourrigat) on hypoellipticity for left invariant vector fields on graded nilpotent Lie groups. Helffer and Nourrigat proved several cases of the conjecture, but it has become newly accessible thanks to a beautiful observation by Debord and Skandalis which characterizes classical pseudodifferential operators in terms of Connes’ tangent groupoid. We will discuss how groupoidal methods can be used to resolve the Helffer- Nourrigat conjecture. This talk is based on joint work with E. Van Erp, with I. Androulidakis and O. Mohsen, and with N. Couchet.
