Orateur
Dr
Marco Vitturi
(Laboratoire Jean Leray, Université de Nantes)
Description
Affine measures have been introduced in the past to facilitate the study of Fourier Restriction and the related question of the L^p smoothing properties of averages along submanifolds (convolution Radon transforms). They capture in a geometric way the role of curvature. In this talk we present the Affine Measures and then discuss the geometric interpretation of these objects - a line of research that started with a result of D. Oberlin relating such measures to a Hausdorff-like ambient measure. We discuss some new results in the same spirit (this is joint work w/ J. Hickman): in particular, we give a geometric interpretation for the case of hypersurfaces with vanishing curvature. If time allows, we discuss how one could move on to study certain non-translation-invariant cases.
