Rational points on elliptic curves
The goal of this seminar is to introduce the study of the arithmetic and geometry of a particular family of Diophantine equations: elliptic curves. They are a central object in modern number theory, and that is the perspective we will take. While the study of elliptic curves naturally calls for some basic tools from algebraic geometry, no prior knowledge of the subject will be assumed — we will develop the necessary background as we go.