Speaker: Niven Achenjang

Title: Overview of the Lawrence-Venkatesh proof

Abstract:

The Mordell Conjecture states that a curve of genus $g\ge2$ over a number field can only have finitely many rational points. This was first proved by Faltings in his famous 1983 paper, but more recently, a new proof was given by Brian Lawrence and Akshay Venkatesh using $p$-adic methods. In this talk, after briefly setting up the context of Mordell's conjecture, we will discuss, in broad strokes, the various ideas and results which go into the Lawrence-Venkatesh proof.

References:

$\bullet$ Poonen, A $p$-adic approach to rational points on curves

$\bullet$ Poonen, $p$-adic approaches to rational and integral points on curves

$\bullet$ Lawrence and Venkatesh, Diophantine problems and $p$-adic period mappings