abstract: I will describe some geometric configurations (bi-arrangements of hyperplane and toric type) whose associated cohomology groups encapture arithmetic datum about values of the Riemann zeta function at integers, and classical polylogarithms. In particular, we will see how topological and combinatorial methods allow one to compute the coefficients of some linear forms in zeta values that are related to problems in diophantine approximation. This is partly joint with Javier Fresàn (ETHZ).