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Gerhard Frey

Gerhard Frey Gerhard Frey is a professor at Universität Duisburg-Essen, Germany. He is widely known for his work in Number Theory. His Frey curve was central to Wiles' proof of Fermat's Last Theorem. Frey was co-editor of the Manuscripta Mathematica. He was awarded the Gauss medal of the Braunschweigische Wissenschaftliche Gesellschaft in 1996 for his work on Fermat's Last Theorem. Since 1998, he has been a member of the Göttingen Academy of Sciences. In 2006 Frey received the Certicom ECC Visionary Award for his contributions to Elliptic Curve Cryptography. His research areas are Number Theory and Arithmetical Geometry, with applications to Coding Theory and Cryptography.

 

"Elliptic Curves in Theory and Practice": Elliptic curves E over fields K are fascinating objects for mathematical research. On the one hand, they are very simple objects, namely cubic curves in the projective plane and so easily accessible for elementary approaches. On the other side, they are abelian varieties of dimension one and so the deep theory of these objects can be used, too. A particular, the K-rational points on elliptic curves form an abelian group E(K). This gives rise to a very interesting aspect: The operation of the Galois group on K on algebraic points of E yields representations that carry a lot of information both about the field K and the curve E. A spectacular consequence is Wiles proof of Fermat's Last Theorem. But this is only part of the reason for the high interest in elliptic curves nowadays. Based on the theory of elliptic curves there is a strong algorithmic aspect that has surprisingly far going applications in data security and is one of the backbones of public key cryptography.