A Two Dimensional Delta Symbol Method and Applications

Explore a mathematical conference talk presenting a novel two-dimensional delta symbol method and its applications to number theory. Learn about the extension of the classical delta symbol developed by Duke-Friedlander-Iwaniec and Heath-Brown, which has been instrumental in studying rational points on hypersurfaces of low degrees. Discover how this new two-dimensional approach enables the establishment of a quantitative Hasse principle for smooth intersections of two quadratic forms defined over Q in at least ten variables. Understand the underlying goal of these delta symbols: to perform a double Kloosterman refinement of the circle method, a sophisticated technique in analytic number theory. The presentation draws from collaborative research with Simon Rydin Myerson and Pankaj Vishe, offering insights into cutting-edge developments in the field of arithmetic geometry and the study of Diophantine equations.