Elliptic curves are among the most beautiful and important objects in modern mathematics. At first glance, they are simply smooth cubic curves in the plane, but they quickly reveal a rich structure: they form groups, connect geometry with number theory, and play a central role in deep results such as the proof of Fermat’s Last Theorem. In this seminar, we will build up the foundations of the subject. We will learn how to describe elliptic curves algebraically and geometrically, study their rational points and group law, and explore tools such as heights, reduction modulo primes, and the Mordell–Weil theorem. The seminar is intended for students with some background in algebra and number theory.
- begleitende Lehrperson: Gautier Jean Christian Ponsinet
- verantwortliche Lehrperson: Xiaoyu Zhang
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