Benjamin Bruce

University of Wisconsin, Madison

Talk Title: Toward endpoint Fourier restriction to a perturbed hyperbolic paraboloid

Abstract: We discuss recent work on Fourier restriction to hyperbolic (negatively curved) surfaces.  Certain difficulties arise in the hyperbolic setting (relative to the elliptic), leading to development of new techniques.  Recent results of Buschenhenke-Müller-Vargas suggest that applying these techniques on the hyperbolic paraboloid may be simpler than on perturbations thereof.  In this talk, we will describe one way in which the perturbed case is “better” and state some progress toward catching it up to that of the hyperbolic paraboloid.