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Matthias Flach

Professor of Mathematics
Matthias Flach whiteboard
Contact information for Matthias Flach
Contact Method Value
Mail Code: MC 253-37
Office: 264 Linde Hall (37)
Phone: 626-395-4343
Dipl., Johann-Wolfgang von Goethe University (Frankfurt), 1986; Ph.D., St. John's College, 1991. Associate Professor, Caltech, 1995-99; Professor, 1999-. Executive Officer for Mathematics, 2006-09.
Research Areas: Mathematics

Research Interests

Arithmetic algebraic geometry, in particular, special values of L-functions (conjectures of Bloch, Beilinson, Deligne, Bloch-Kato), Galois module theory, motivic cohomology

B.A., J.W. Goethe Universität, Frankfurt, Germany, 1986
Ph.D., University of Cambridge, U.K., 1991

Matthias' work is in Arithmetic Algebraic Geometry. In particular his research focuses on special values of L-functions and the conjectures of Beilinson, Deligne, Bloch/Kato and Fontaine/Perrin-Riou. His recent results include a complete proof of the equivariant Tamagawa number conjecture for Dirichlet L-functions and new cases of the local Tamagawa number conjecture over tamely rami ed elds. In joint work with B.Morin he has been developing an idea originally due to Lichtenbaum (Weil-etale cohomology) which focuses on Zeta functions of arithmetic schemes rather than motivic L-functions and draws clear connections to Arakelov theory and Deningers ideas on motivic L-functions. The near term goal in this area is to nd precise special value conjectures independent of p-adic Hodge theory.

Matthias has also published about cohomology of topological groups. His mathematical interests include Galois module theory, algebraic K-theory and motivic cohomology, categorical algebra, topos theory and algebraic topology.

Selected Publications

  • (with D. Burns) On Galois structure invariants associated to Tate motives
    Click for the pdf file of this paper.
  • Euler characteristics in relative K-groups
    Click for the pdf file of this paper.
  • The equivariant Tamagawa number conjecture: A survey (with an appendix by C. Greither)
    Click for the pdf file of this paper.