Dr. Matthias Flach

Biography

Matthias Flach is a professor at the California Institute of Technology, specializing in Arithmetic Algebraic Geometry. His research primarily focuses on special values of L-functions and their conjectures, including those proposed by Bloch, Beilinson, and Deligne, along with Galois module theory and motivic cohomology. Flach has contributed significantly to the proof of the equivariant Tamagawa number conjecture for Dirichlet L-functions and has investigated new cases of local Tamagawa number conjectures in tamely ramified fields. His work also involves the development of concepts originally posited by Lichtenbaum in relation to Weil-étale cohomology, emphasizing the connections between zeta functions of arithmetic schemes and motivic L-functions. Additionally, he explores algebraic K-theory, categorical algebra, topos theory, and algebraic topology.

Research Interests