Aspects of quadratic Chabauty via modular formsMPIM

by Isabell Rendell (MPIM)

Wednesday Nov 18, 2026, 3:00 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

Quadratic Chabauty is one of the most successful recent methods in computing rational points on modular curves. The current algorithm requires an explicit plane model of the curve, which becomes inefficient to compute with when the genus is sufficiently large. In joint work with Marius Leonhardt, we compute the first steps of quadratic Chabauty - a basis of de Rham cohomology and certain Hodge filtration - without requiring any plane models. We have implemented our method on the non-split Cartan modular curves with levels N=25, 29, which have genus 14 and 24 respectively, whose rational points are not currently known.