Unexpected quadratic points of hyperelliptic curves via Chabauty-Coleman bound for surfaces 

A celebrated result of Coleman gives a completely explicit version of Chabauty's finiteness theorem for rational points in curves over a number field, by a study of zeros of p-adic analytic functions. After several developments around this result, the problem of proving an analogous explicit bound for higher dimensional subvarieties of abelian varieties remains elusive. 

In this talk, I'll sketch the proof of such a bound for surfaces contained in abelian varieties. This is joint work with Hector Pasten.

Additionally, I'll present an application of this method to give an upper bound for the number of unexpected quadratic points of hyperelliptic curves of genus 3 defined over Q. This is joint work in progress with Jennifer Balakrishnan.