(1) Obtain an expression of zeta values of convex cones using multiple L-values.

Let C be a rational finitely generated convex cone and l_1, ... ,l_k be rational linear forms which take positive values on the interior of C. For an integer point z of C, we consider the inverse L(z) of the products of l_1(z),...l_k(z). We take a sum of L(z), where z runs through all the integer points in the interior points of C and get the L-values for a convex cone. We showed that this can be expressed as a rational linear combination of multiple L-values. In the proof we gave an integral expression of this L-values, which can be interpreted as a relative cohomology of complex tori.


(2) Construction of big algebra on which Grothendieck-Teichmuller group acts.

The Grothendieck-Teichmuller group acts on the fundamental group of moduli space of n-points in the projective line. We want to construct large class of varieties, and homomorphisms whose relative cohomology has a natural action of Grothendieck-Teichmuller group. Using these construction, we want to construct big (non-commutative) algebra with an action of Grothendieck-Teichmuller group.