Omar Mohsen
Biography
Shot bio: Paris-Saclay University.
Title: On maximally hypoelliptic differential operators.
Abstract:
The class of Maximally hypoelliptic differential operators is a large class of differential operators that contains elliptic operators as well as Hörmander's sum of squares operators. I will present our work where we define a principal symbol generalising the classical principal symbol for elliptic operators. I will then state our main theorem showing 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. This is joint work with Androulidakis and Yuncken.
In the second part of the talk I will present a topological index formula for the analytic index of maximally hypoelliptic differential operators on compact manifolds. In the end I will give some examples of index computations using such formula.
