## EVENT DETAILS AND ABSTRACT

**Number Theory**
**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.

**Date:** Monday, March 4, 2019

**Time:** 4:00PM

**Where:** Lunt 107

**Contact Person:** Brett Frankel

**Contact email:** brettf@math.northwestern.edu

**Contact Phone:**

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