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Semiclassical analysis on filtered manifolds

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GSTW01 - High energy spectral theory: geometry and dynamics

In this talk, we will discuss the construction of pseudodifferential operators on filtered manifolds and the semiclassical approach of partial differential equations (PDEs) that it allows. Indeed, a natural example of filtrations of the tangent space of a manifold is the one generated by the set of vector fields involved in the hypoellipticity of an operator via the Hörmander condition. Thus, there is a tight link between filtered manifolds and these operators, and it is not surprising that a pseudodifferential calculus adapted with the filtration is adequate for studying PDEs involving this operator. We will carefully define the items involved in the construction, and develop examples. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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