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. 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. Elliptic curves also have come to play an important role in modern cryptography, and they continue to be extensively studied for possible future crypto systems resistant to quantum computing. Hands-on approach based on exploring examples rather than giving formal proofs will be followed by all instructors.
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Scientific program is available on the local website of the school:
https://sites.google.com/view/ecasummerschool2025
Official language of the school: english