BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Fractional Laplacians and extension problems: the higher rank case (Joint with Maria del Mar Gonzalez): Saez, Mariel


The aim of this talk is to define conformal operators that arise from an extension problem of co-dimension two. To this end we interpret and extend results of representation theory from a purely analytic point of view. In the first part of the talk I will give definitions and interpretations of the fractional Laplacian and the conformal fractional Laplacian in the general framework of representation theory on symmetric spaces and also from the point of view of scattering operators in conformal geometry. In the second part of the talk I will show constructions of boundary operators with good conformal properties that generalise the fractional Laplacian in $\mathbb R^n$ using an extension problem in which the boundary is of co-dimension two. Then we extend these results to more general manifolds that are not necessarily symmetric space

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