06.06.2023, 15 Uhr
Phenomena in High Dimensions
Pierre Youssef (New York University, Abu Dhabi)
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.
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