##### Pavel Coupek, March 19, 2024

**Abstract.** The Chabauty-Coleman method and quadratic Chabauty are p-adic methods that aim to determine the set of all rational points of a smooth projective curve of genus at least 2, assuming certain inequalities involving invariants of its Jacobian. I will describe a geometric approach to quadratic Chabauty developed by Edixhoven and Lido over the rational numbers, and an extension of this method to the case of a general number field. The latter part is joint work with David Lilienfeldt, Luciena X. Xiao and Zijian Yao.