Geometric quadratic Chabauty without equations II: Explicit Methods

We discuss a geometric quadratic Chabauty algorithm for the normalizers of non-split Cartan modular curves of prime level. The method approaches the problem of finding rational points from a modular point of view: in particular, we do not use defining equations for the curves. In this talk we focus on the explicit method applied to non-split Cartan curves. We will also showcase the example of the level 13 curve. This is joint work with Khuri-Makdisi, Lido, Lombardo, Mascot, and Parent.