We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
"A geometric version of the circle method." Ann. of Math. (2) 191 (3) 893 - 948, May 2020. https://doi.org/10.4007/annals.2020.191.3.4