Jennifer Balakrishnan (Boston University)

Title:  Quadratic Chabauty for modular curves 

Abstract: By Faltings' theorem, the set of rational points on a curve of genus 2 or more is finite. We give a survey of the quadratic Chabauty method, which is used to determine a finite superset of the set of rational points for certain curves of genus 2 or more. In particular, we discuss what aspects of quadratic Chabauty can be made practical for certain modular curves and highlight several examples, including the non-split Cartan modular curve of level 27. This is based on joint work with Alexander Betts, Netan Dogra, Daniel Hast, Aashraya Jha, Steffen Mueller, Jan Tuitman, and Jan Vonk.