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

algebraic geometrynumber theory

Audience: advanced learners

( slides )

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STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.

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