Motivic cohomology and values of zeta functions
Motivic L-functions and Galois module structures.
Motivic measures
Multicanonical systems of elliptic surfaces in small characteristics
Multiple Bernoulli series, an Euler-MacLaurin formula, and Wall crossings
We study multiple Bernoulli series associated to a sequence of vectors generating a lattice in a vector space. The associated multiple Bernoulli series is a periodic and locally polynomial function, and we give an explicit formula (called wall crossing formula) comparing the polynomial densities in two adjacent domains of polynomiality separated by a hyperplane. We also present a formula in the spirit of Euler-MacLaurin formula. Finally, we give a decomposition formula for the Bernoulli series describing...
Multiple zeta values and periods of moduli spaces
We prove a conjecture due to Goncharov and Manin which states that the periods of the moduli spaces of Riemann spheres with marked points are multiple zeta values. We do this by introducing a differential algebra of multiple polylogarithms on and proving that it is closed under the operation of taking primitives. The main idea is to apply a version of Stokes’ formula iteratively to reduce each period integral to multiple zeta values. We also give a geometric interpretation of the double shuffle...
Multiplikative Untergruppen in abeloiden Mannigfaltigkeiten.