Course overview
This course will serve as an introduction to the theory of elliptic and hyperelliptic curves, and in particular, will explore how explicit computation can aid in our understanding of several open questions and conjectures in number theory. We will begin with an overview of elliptic and hyperelliptic curves; further topics will include algorithms for zeta and L-functions, arithmetic statistics and databases of curves, finding rational points on curves, and computations motivated by the Birch and Swinnerton-Dyer conjecture. Throughout, we will make use of various computational packages, such as those available in Sage and Magma. We will also try our hand at a few new large-scale computations using SageMathCloud or Google Compute Engine.Evaluation
There will be homework assignments (60%) and a final project (40%).Problem set 1, due February 1
Problem set 2, due February 8
Problem set 3, due February 20
Problem set 4, due March 3
Problem set 5, due March 29
Problem set 6, due April 19