Some aspects of groupoid techniques for pseudodifferential operators (PDOs)

28.05.2021, 11:00  –  Online Seminar
Arbeitsgruppenseminar Analysis

Malte Leimbach (Uni Potsdam)

Following van Erp's and Yuncken's "Groupoid approach to pseudodifferential operators" I will discuss how one can use Connes' tangent groupoid and the "zoom-action" to define PDOs. I will point out some geometric aspects of the tangent groupoid which play an important role in the background of this approach, in particular the connection and the groupoid exponential. I will present van Erp's and Yuncken's construction of the full symbol of their PDOs by using a Taylor-like expansion and by this, we will see that their PDOs are exactly the classical PDOs on the manifold. If time admits, I will mention the obstructions (on the connection) to defining the tangent groupoid in the case of a filtered manifold which allows to generalize the definition of PDOs to this setting.

Forthcoming speakers are  Alfonso Garmendía on June 4th, Konrad Waldorf on June 11th, Lashi Bandara on June 18th, Bernadette Lessel on July  2nd and Ihsane Malass on July 9th.
You are welcome to suggest speakers or topics for  forthcoming sessions.

You are welcome to invite your friends and colleagues to join us! If you wish to attend the talks,  please contact Sylvie Paycha paycha@math.uni-potsdam.de for the login details.