09-02-2017. Seminari d'edps i aplicacions. Mariel Sáez (Universidad Católica de Chile) " Fractional Laplacians and extensions problems: the higher rank case. 15 h. Aula S01. FME

Jan 25, 2017

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 spaces. (Joint work with M. Mar González)