Orateur
Description
The study of pseudodifferential operators on Lie groupoids offers a natural extension of classical analysis on smooth manifolds, encompassing singular spaces. Moreover, pseudodifferential operators can be generalized in the classical setting by Fourier integral operators. A key result in this context is Egorov’s theorem: conjugation by a Fourier integral operator preserves pseudodifferential operators. Duistermaat and Singer later established a converse: any automorphism of the filtered algebra of classical pseudodifferential operators can be realized as conjugation by a Fourier integral operator.
In this talk, I will discuss a generalization of this result in the setting of Lie groupoids. This involves a detailed examination of the symplectic structure of the cotangent groupoid, which is fundamental for constructing Fourier integral operators in this context.
