Karl Rubin

Karl Rubin ( born January 27, 1956 in Urbana, Illinois) is an American mathematician who works in arithmetic algebraic geometry and number theory.

Life

Rubin studied at Princeton, where he graduated with a Bachelor in 1976. Then he made in 1977 in Harvard master's degree and his doctorate there in 1981 Andrew Wiles with On the arithmetic of CM Elliptic Curves in Zp Extensions ( with CM Elliptic Curves are those meant by complex multiplication). In 1982 he was a lecturer at Princeton, 1984, assistant professor at Ohio State University, where he was professor from 1987 to 1999 ( 1988/9 also at Columbia University). 1997 to 2006 he was a professor at Stanford and is currently Thorp professor at the University of California at Irvine.

Rubin expanded the theory introduced by Victor Kolyvagin Euler systems and applied them in arithmetic algebraic geometry. He was the first one (1986 ) was able to prove the finiteness of the Tate - Shafarevich groups for specific elliptic curves over the rational numbers and thus also made progress in the still open conjecture of Birch and Swinnerton - Dyer. He also demonstrated with these methods, the main assumptions of the Iwasawa theory in imaginary quadratic number fields.

In addition, it also deals with cryptographic applications of elliptic curves and their generalizations.

In 1975 he was Putnam Fellow, Sloan Fellow in 1985, 1994 Guggenheim Fellow and received the 1988 National Science Foundation Presidential Young Investigator Award. In 1992 he received the Cole prize in number theory. In 2002 he was invited speaker on the ICM in Beijing. In 1999 he received the Humboldt Award of the Alexander von Humboldt Foundation. He is a Fellow of the American Mathematical Society.

Writings

  • Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton - Dyer, Inventiones mathematicae 64, 1981, p 455-470 (English)
  • Elliptic curves and Zp -extensions, Compositio Mathematica 56, 1985, p 237-250 (English)
  • Local units, elliptic units, Heegner points and elliptic curves, Inventiones mathematicae 88, 1987, p 405-422 (English)
  • Global units and ideal class groups, Inventiones mathematicae 89, 1987, p 511-526 (English)
  • Tate - Shafarevich groups of elliptic curves with complex multiplication in John Coates et al. (Ed.): Algebraic number theory - in honor of K. Iwasawa, Academic Press, Boston, 1989, ISBN 0-12-177370-1, pp. 409-419 (English; series Advanced Studies in Pure Mathematics 17)
  • The main conjecture, Appendix in Serge Lang: Cyclo Tomic Fields I and II, Springer- Verlag, 1990, ISBN 3-540-96671-4, pp. 397-419 (English; series Graduate Texts in Mathematics 121)
  • The "main conjectures " of Iwasawa theory for imaginary quadratic fields, Inventiones mathematicae 103, 1991, pp. 25-68 (English)
  • P- adic L -functions and rational points on elliptic curves with complex multiplication, Inventiones mathematicae 107, 1992, pp. 323-350 (English)
  • Euler system and exact formulas in number theory, Annual Report of the DMV 98, 1996, pp. 30-39 (English)
  • Euler systems and modular elliptic curves (PDF file, 243 kB) in Anthony J. Scholl, RL Taylor ( ed.): Galois representations in arithmetic algebraic geometry, Cambridge University Press, Cambridge 1998, ISBN 0-521-64419-4, pp. 351-367 (English; series London Mathematical Society Lecture Note Series 254)
  • Euler systems, Princeton University Press, Princeton, 2000, ISBN 0-691-05075-9 (English)
  • Alice Silverberg: Ranks of Elliptic Curves, Bulletin of the AMS 39, 2002, pp. 455-474 (English)
  • With Barry Mazur: Elliptic curves and class field theory in Tatsien Li (ed.). Proceedings of the ICM Beijing 2002 Vol II: Invited Lectures, Higher Education Press, Beijing 2002, ISBN 7-04-008690-5, p 185-196 (English)
  • With Barry Mazur: Kolyvagin Systems, American Mathematical Society, 2004, ISBN 0-8218-3512-2 (English; series Memoirs of the AMS 168)
Urbana (Illinois) Princeton (New Jersey) Harvard University Irvine, California Birch and Swinnerton-Dyer conjecture John H. Coates Richard Taylor (mathematician)
466305
de