A circle method for algebraic geometers

Browning and Vishe studied the moduli space of smooth genus zero curves of fixed degree on a smooth low-degree hypersurface using the circle method, a technique from analytic number theory. I’ll explain how their strategy can be interpreted completely algebro-geometrically, and then use this perspective to generalize their results to the higher genus setting. Time permitting, I’ll also discuss some applications to Geometric Manin’s conjecture and terminal singularities of these moduli spaces, the latter of which is joint work with Jakob Glas.