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 ramied 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.