About this Event
182 MEMORIAL DR, Cambridge, MA 02139
https://researchseminars.org/seminar/STAGESpeaker: Bjorn Poonen (MIT)
Title: Siegel's method
Abstract:
We will show how theorems about diophantine approximation (e.g., Roth's theorem that irrational algebraic numbers cannot be approximated too well by rational numbers) can be used to prove one of the most famous theorems of 20th century arithmetic geometry, Siegel's theorem that a hyperbolic affine curve can have only finitely many integral points. The proof is ineffective, however: 95 years later it is still not known if there is an algorithm that takes as input the equation of a curve and returns the list of its integral points.
Reference: Chapter 7 of Serre, Lectures on the Mordell-Weil theorem.