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Difusión no lineal en Madrid
Seminario conjunto de las universidades: UAM, UC3M, UCM, UPM y URJC
Fractional Laplacians and extension problems:
the higher rank case
Prof. Mariel Sáez
Pontificia Universidad Católica de Chile
Jueves 16 de febrero, 12:30
Seminario del Departamento de Matemáticas, aula C-17-520
U. Autónoma de Madrid
Resumen. The aim of this talk is to define non-local 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 generalize the fractional Laplacian in 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 María del Mar González
Organizado por los proyectos: MTM2014-52240-P, MTM2014-53037-P y Fundación BBVA para Investigadores y Creadores Culturales 2016
Comité organizador: Matteo Bonforte, Mar González, Arturo de Pablo y Fernando Quirós