Matthias Flach (mathematician)

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

Flat studied after high school in 1981 at the Goethe University in Frankfurt am Main with a graduate degree in 1986 and from 1987 to 1990 at the University of Cambridge, where he earned 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 an associate professor and in 1999 professor at Caltech.

In 2004 he was a visiting professor at Harvard University.

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

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

He works for example David Burns from King's College London together.

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

He is married and has two children.

Writings

  • 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, Vol 305, 1996, pp. 65-102
  • 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., Volume 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, p, 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
John H. Coates L-function Sloan Fellows
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