Shantanu Dave (University of Vienna)
A filtered manifold is a manifold with a graded (noncommutative) group structure on its tangent space. These include familiar examples of foliations and contact structures. The new group structure on the tangent space plays a crucial role in understanding the hypoellipticity of natural operators on the given manifold. Most general and elegant way to study pseudodifferentail operators on filtered manifolds is due to Yuncken and van Erp using a Heisenberg tangent groupoid.
This talk will briefly recall the Heisenberg tangent groupoid and the calculus of pseudodifferential operators. Then we will consider a manifold M with different filtrations with some noncommutative group structure on the tangent space. (This group is usually referred to as the osculating group). We will discuss how the knowledge of hypoellipticity can be transferred from one filtered manifold to the other.
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