|Date||Nov 29, 2017|
In this talk, we introduce the connection between additive energy estimates and the extension problem for paraboloids in the finite field setting. We improve additive energy estimates for subsets of paraboloids in even dimensional vector spaces over finite fields. As a consequence, up to endpoint, we obtain the optimal L^2 → L^r extension estimates for paraboloids in even dimensions d ≥ 6. This is a joint work with Alex Iosevich and Mark Lewko.