Elliptic curves and their applications

July 14-26, 2025

Yerevan, Armenia

About

The goal of the summer school is to introduce students and junior scientists to the basics of the theory of elliptic curves and their applications in modern number theory and cryptography.

The origins of the theory of elliptic curves go back to the 19th century, but it has become a central area of number theory only in the 20th century with the work of Mordell, Hasse, Weil and many others. A particularly prominent developments were the formulation of the conjecture of Birch and Swinnerton-Dyer, and the discovery of connections between elliptic curves and modular forms. The celebrated proof of Fermat’s Last Theorem by Wiles is the first general result on the modularity of elliptic curves – a topic which is still very much at the forefront of research in number theory. Elliptic curves also have come to play an important role in modern cryptography, and they continue to be extensively studied for possible future cryptosystems resistant to quantum computing.

Summer School in the News

Mini-Courses and Instructors

Introduction to Cryptography (Diana Davidova, Institute of Mathematics of the National Academy of Sciences of Armenia)
Elliptic Curves and Modular Forms (Valentijn Karemaker, Utrecht University)
Introduction to Elliptic Curves (Mihran Papikian, Pennsylvania State University)
Elliptic Curves and Cryptography (Fabien Pazuki, University of Copenhagen)

Algebra and Number Theory This course was taught online by Mihran Papikian in Fall semester of 2024. It covered the basic notions of abstract algebra with a view toward applications in number theory. It was intended as a preparation for Armenian undergraduate students for the CIMPA summer school. The lecture notes (in English) and the recordings of the lectures (in Armenian) are available at the above website.