An explicit study of a family of cellular integrals

Abstract

We express a family of basic cellular integrals over moduli spaces of curves explicitly in terms of multiple zeta values, answering a question of Brown. Moreover, we study a priori the weights appearing in these integrals and find a relation that expresses the odd-dimensional integrals in terms of the even-dimensional ones. We also sketch an explanation of this relation in the spirit of Grothendieck's Period Conjecture.

36 pages. Corrected a mistake in the statement of the main result due to a wrong definition of ${\psi }_n$ in Section 2.4. Comments welcome!