Gerhard Frey (mathematician)

from Wikipedia, the free encyclopedia
Gerhard Frey 2004 in Oberwolfach

Gerhard Frey (born June 1, 1944 in Bensheim ) is a German mathematician who mainly works in the field of number theory .

Career

After graduating from high school in Tübingen in 1963 , Frey studied mathematics and physics at the University of Tübingen and graduated in 1967. He received his doctorate in 1970, and in 1973 his habilitation followed . After an assistant professorship in Heidelberg from 1969 to 1973 and a professorship at the University of Erlangen-Nuremberg from 1973 to 1975, as well as a professorship in Saarbrücken from 1975 to 1990, he held a chair for number theory at the Institute for Experimental Mathematics at the University of Duisburg until 2009 -Eat in food . He was visiting scholar at various universities and research institutions, such as Ohio State University , Harvard University , the University of California at Berkeley , the Mathematical Sciences Research Institute (MSRI), the Institute for Advanced Studies at the Hebrew University Jerusalem , and the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro .

Work area

Frey became known through the assumption made in 1986 that a counterexample

for Fermat's great theorem an elliptic curve with the equation

that would contradict the Taniyama-Shimura conjecture .

Frey's conjecture was proven that same year by the American mathematician Kenneth Alan Ribet . In 1995 Andrew Wiles and Richard Taylor showed that the Taniyama-Shimura conjecture is true in the crucial cases; so there is no counterexample as above, i.e. H. the Fermatsche theorem is true.

His research areas are arithmetic properties of function fields over finite fields , as well as properties of representations of Galois groups over the rational numbers . In addition, he deals with the calculation of the L-series of number fields and curves and, related to this, module forms .

He also deals with Elliptic Curve (ECC) cryptography . In 1994 he and Hans-Georg Rück found a method of attacking the discrete logarithm problem in elliptical curves ( ECDLP ) with Weil and Tate pairings and in 1998 on the Weil descent .

Honors and prizes

In 1996 he received the Gauss Medal of the Braunschweigische Wissenschaftliche Gesellschaft for his contribution to Fermat's theorem. Since 1998 he has been a member of the Academy of Sciences , Göttingen. The Department of Mathematics at the University of Kassel awarded Gerhard Frey an honorary doctorate in 1999 "in recognition of his outstanding contributions to the advancement of mathematics". The Faculty of Mathematics and Physics in Tübingen awarded its former student an honorary doctorate in 2007 "for his groundbreaking discoveries in the number theory of elliptical curves and for his decisive contributions to the solution of the problem of the century - known as Fermat's last theorem". In 2014 he received an honorary doctorate from Saarland University .

Fonts

Elementary number theory , Wiesbaden 1994, ISBN 978-3-528-07256-8 , doi : 10.1007 / 978-3-322-88793-1

Web links

Individual evidence

  1. ↑ a b Braunschweigische Wissenschaftliche Gesellschaft: Jahrbuch 1996 , Göttingen 1997, p. 223
  2. ↑ Frey, Links between stable elliptic curves and certain diophantine equations. Annales Universitatis Saraviensis. Series Mathematicae 1, 1986, pp. 1-40.
  3. ↑ Frey, Rück A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Mathematics of computation, Vol. 62, 1994, pp. 865-874.
  4. ↑ Frey Application of arithmetical geometry to cryptographic constructions , Proc. 5th International Conference on Finite Fields and Applications, Springer 2001, pp. 128-161.
  5. ^ Braunschweigische Wissenschaftliche Gesellschaft: Jahrbuch 1996 , Göttingen 1997, p. 222
personal data
SURNAME Frey, Gerhard
BRIEF DESCRIPTION German mathematician (number theory)
DATE OF BIRTH June 1, 1944
PLACE OF BIRTH Bensheim