Quadratic Chabauty, p-adic adelic metrics and local contributions

This talk is based on my ongoing work with Steffen Muller and Padma Srinivasan. I will explain the idea of the Quadratic Chabauty method for finding rational points on curves and how one reinterprets previous work by Balakrishnan and Dogra, on their own and with collaborators, using p-adic adelic metrics on line bundles. Time permitting I will explain how one can use this to compute the “local contributions away from p” for Quadratic Chabauty, which are crucial for computations.