EVENT DETAILS AND ABSTRACT

Title: The geometry of the unipotent Albanese map
Speaker: Daniel Hast
Speaker Info: Rice University
Brief Description:
Special Note:
Abstract:

Given a curve of genus at least 2 over a number field, Faltings' theorem tells us that its set of rational points is finite; however, provably computing the set of rational points remains a major open problem in general, as does the question of whether the number of rational points can be uniformly bounded. We will survey some recent progress and ongoing work using the Chabauty–Kim method, which uses the fundamental group to construct p-adic analytic functions that vanish on the set of rational points. In particular, we present a new proof of Faltings' theorem for superelliptic curves over the rational numbers (due to joint work with Jordan Ellenberg), and a conditional generalization of the Chabauty–Kim method to real number fields and higher dimensions.