Algebra/Topology seminar

Speaker: Johan Alm (Stockholm)

Title: The Gravity cooperad is cofree

Abstract: We show that the Gravity cooperad, formed by the cohomologies of the 
open moduli spaces of curves of genus zero and with Poincaré residue as 
cocomposition, is the linear hull of a cofree nonsymmetric cooperad of 
sets. This has a number of consequences. First of all, it implies that 
the mixed Hodge structure on the degree k cohomology of Francis Brown's 
partial compactification of the moduli space is pure of weight 2k. 
Secondly, it implies that any (formal) period integral on the moduli 
space has a "renormalization" to an honest integral, converging to a 
linear combination of multiple zeta values. The results are part of 
joint work with Dan Petersen.