Isabel Rendell

Quadratic Chabauty for Modular Curves

Quadratic Chabauty refers to the 'depth two' case of the Chabauty-Kim method, which can be viewed as a generalisation of the Chabauty-Coleman method. In recent years, Quadratic Chabauty has been used to explicitly compute the set of rational points, $X(\mathbb{Q})$, for various modular curves $X$. I will start the talk by discussing the problem of finding $X(\mathbb{Q})$ for a 'nice' curve of genus at least 2, and then give an overview of the Chabauty-Coleman method before finishing with Quadratic Chabauty. Throughout the talk I will try and assume as few prerequisites as possible and demonstrate methods by examples.