Matthias Flach (mathematician)

from Wikipedia, the free encyclopedia

Matthias Flach (* 1963 ) is a German mathematician who deals with arithmetic algebraic geometry and number theory.

After graduating from high school in 1981, Flach studied at the Goethe University in Frankfurt am Main with a diploma in 1986 and from 1987 to 1990 at the University of Cambridge , where he did his doctorate under John Coates ( Selmer groups for the symmetric square of an elliptic curve ). 1989 to 1994 he was an assistant at the University of Heidelberg and 1994/95 assistant professor at Princeton University . From 1995 he was Associate Professor and from 1999 Professor at Caltech .

In 2004 he was visiting professor at Harvard University .

He deals with special values ​​of L-functions and related conjectures by Spencer Bloch , Alexander Beilinson , Pierre Deligne and Kazuya Kato , theory of Galois modules and motivic cohomology.

An Euler system constructed by Flach (introduced by Victor Kolyvagin in the late 1980s) and the methods used for it played an important role in the proof of the Fermat conjecture (or Shimura-Taniyama conjecture) by Andrew Wiles .

He works with David Burns from King's College London , among others .

In 1995 he received the Heinz Maier-Leibnitz Prize . From 1996 to 2000 he was a Sloan Research Fellow .

He is married and has two children.

Fonts

  • A finiteness theorem for the symmetric square of an elliptic curve, Inventiones Mathematicae, Volume 109, 1992, pp. 307-327
  • with D. Burns: Motivic L-functions and Galois module structures, Mathematische Annalen, Volume 305, 1996, pp. 65-102
  • with D. Burns: On Galois structure invariants associated to Tate motives, Amer. J. Math., Vol. 120, 1998, pp. 1343-1397.
  • with D. Burns: Tamagawa numbers for motives with (non-commutative) coefficients, Documenta Mathematica, Volume 6, 2001, pp. 501-569, Part 2, American Journal of Mathematics, Volume 125, 2003, pp. 475-512
  • Euler characteristics in relative K-groups, Bull. London Math. Soc., Vol. 32, 2000, pp. 272-284.
  • with F. Diamond, L. Guo: The Bloch-Kato conjecture for adjoint motives of modular forms, Math. Res. Letters, Volume 8, 2001, pp. 437-442.
  • with F. Diamond, L. Guo: The Tamagawa number conjecture of adjoint motives of modular forms, Ann. Scient. Ecole Normale Superieure, Volume 37, 2004, pp. 663-727.
  • The equivariant Tamagawa number conjecture: a survey, in D. Burns (editor) Stark's conjecture. Recent work and new directions , Contemporary Mathematics, Volume 358, 2004
  • Cohomology of Topological Groups with applications to the Weil Group, Compositio Math., Volume 144, 2008, No 3
  • Iwasawa Theory and Motivic L-functions, Pure and Appl. Math. Quarterly, Jean Pierre Serre special issue, part II, Vol. 5, no.1, 2009

Web links

Individual evidence

  1. ^ Mathematics Genealogy Project
  2. ↑ Published in Inventiones Mathematicae, Volume 109, 1992, p. 307
  3. ↑ See Euler systems for number fields Encyclopedia of Mathematics, Springer Verlag
  4. ↑ z. B. Eric Weisstein, Taniyama-Shimura-Conjecture
personal data
SURNAME Flat, Matthias
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH 1963