Seminario di analisi matematica
ore
15:30
In this talk, we consider the wave equation where the
Laplacian is replaced by a sub-Laplacian (also called ``Hörmander sum of
square''), which is an hypoelliptic operator. We handle the problem of
describing the propagation of singularities in such equations : the main
new phenomenon that we describe is that singularities can propagate
along abnormal curves at any speed between 0 and 1. This general result
extends an idea due to R. Melrose, and we then illustrate it on an
example, the Martinet case, following a joint work with Y. Colin de
Verdière. Our statements are part of a classical/quantum correspondance
between sub-Riemannian geometry (on the classical side) and the
hypoelliptic operator (on the quantum side), which is also helpful to
interpret results in control theory and spectral theory of hypoelliptic
operators.