Mathematics Colloquium - Prof. Jennifer Balakrishnan, University of Boston

Title: Rational and mock rational points on curves

Abstract:

By a celebrated theorem of Faltings, a curve of genus 2 or more over the rationals has finitely many rational points. While Faltings' proof does not construct the finite set of rational points, Kim's nonabelian Chabauty program gives a finite superset of p-adic

points, known as the Chabauty--Kim sets. We describe the computation of the Chabauty--Kim sets in various settings and examine the mock rational points (those finitely many points that are not rational) that may arise in these sets. Throughout, we present a number of examples.