Title: Counting points on elliptic curves
Speaker: Karl Rubin
Summary:
Elliptic curves are important for both theoretical and practical
reasons, having applications to the proof of Fermat's Last Theorem
and to cryptography. These lectures will introduce elliptic
curves and describe some of the important results, algorithms, and
applications in the field. The three lectures will be organized
as follows.
1. Introduction to elliptic curves: overview and open problems.
2. Counting points over finite fields, and applications.
3. Ranks of elliptic curves: computing the rank, and searching for
curves of large rank.
Prerequisites:
A solid background in basic abstract algebra will be assumed, but
no prior knowledge of elliptic curves is needed.