Title：Principal symbol mapping for Heisenberg groups and/or contact manifolds
Speaker: Dmitriy Zanin（University of New South Wales）
Time: Friday, April 28, 2023, 10:00-11:30
Location:Mingde Building, B201-1
Zoom ID: 882 8540 7533 Password: 028422
Abstract:In this talk, I will introduce the notion of principal symbol. Firstly, in the archaic context of pseudo-differential operators, then in the general C*-algebraic context.Examples to be provided are (a) rather old ones, such as Euclidean spaces and tori (and their non-commutative analogues) and (b) very new ones, such as stratified groups (in particular, Heisenberg groups). I will also demonstrate how does the principal symbol mapping behave under the natural action of diffeomorphisms (in the Euclidean case) and Heisenberg diffeomorphisms (in the Heisenberg group case). This is needed to extend the notion of the principal symbol to the manifolds (from Euclidean case)and to the contact manifolds (from the Heisenberg case).Corresponding globalization theorems will be provided. As an application, I will present the Connes Trace Theorem (including, in particular, the spectrally correct sub-Riemannian volume).
More information about the Functional Analysis Seminar can be found here.
