Lauritz Streck: A geometric approach to counting rational points near curves and hypersurfaces

Speaker
Lauritz Streck, University of Edinburgh

Abstract
We introduce a geometric duality principle and explore its applications to counting rational points near manifolds. For planar and space curves, we give direct proofs improving regularity and endpoints of results by Vaughan-Velani, Beresnevich-Dickinson-Velani, Huang and Chen-Seeger-Srivastava-Technau. We then establish upper bounds for hypersurfaces under the sharp curvature condition of no planar points, previously established by Huang under the assumption of positive Gaussian curvature. In the proof of the hypersurface result, the most difficult cases were established with AI-assistance