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.
Construction of big algebra on which Grothendieck-Teichmuller group
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.