Student AG Seminar: Solvable points on intersections of quadrics, cubics, and quartics

In this talk, we will discuss a recent result of Claudio Gómez-Gonzáles and Jesse Wolfson about solvable points on intersections of hypersurfaces in projective space. In particular, we will give an upper bound on the minimum ambient dimension required to guarantee the density of solvable points on such an intersection. In doing so, we will introduce their method of polar cones and obliteration, and we will see how these results extend and relate to classical questions about solvability in a broader context.