Analysis Seminar

Title: Propagation of singularities in subelliptic PDEs
Speaker: Cyril Letrouit
Speaker Info: MIT
Brief Description:
Special Note: Note unusual time.

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.
Date: Monday, November 28, 2022
Time: 3pm
Where: Lunt 103
Contact Person: Prof. Jared Wunsch
Contact email: jwunsch@math.northwestern.edu
Contact Phone: 847-491-5580
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