The geometric circle method and the cohomology of moduli spaces of rational curves

Vortrag von Dr. Will Sawin

Datum: 12.03.18  Zeit: 13.15 - 14.45  Raum: Y27H25

The Grothendieck-Lefschetz fixed point formula relates the cohomology of varieties over finite fields to their number of points. In many cases, we can use our understanding of the cohomology to prove bounds for the number of points. For the moduli spaces of rational curves on low-degree hypersurfaces, we have a good understanding of the point counts from analytic number theory, and we would like to translate that into cohomological information. This is not possible directly because the spaces can fail to be smooth and always fail to be proper. However, in joint work with Tim Browning, we adapted the classical analytic number theory techniques into a geometric argument to compute the high-degree cohomology groups.