Title of the course: Integral points on elliptic curves
Instructor: Dr. Levent Alpöge
Institution: Harvard University
Dates: 21-27 August 2023
Prerequisites: Linear algebra, group theory, calculus
Level: Advanced undergraduate
Abstract: In the 1600s Fermat would taunt English mathematicians with the following sort of question. Let A and B be integers such that -4A^3-27B^2 is nonzero. Then completely solve the equation y^2 = x^3 + Ax + B in the integers. What I will do in this course is prove Mordell’s great theorem that the set of such solutions is always finite. In the course of the lectures I will explain reduction theory à la Gauss, as well as give a proof of Thue’s theorem in Diophantine approximation. The methods will be elementary, but serious.
Language: English