Johan Alm: On the Rossi-Willwacher family of Drinfel'd associators and multiple zeta values

A Drinfel'd associator is a group-like formal power series in two non-commuting variables, satisfying three deceptively simple conditions, introduced by Vladimir Drinfel'd in 1991. For a long time only two examples were known, the Knizhnik-Zamolodchikov (KZ) associator and its sibling the anti-KZ associator. Carlo Rossi and Thomas Willwacher, building on work by Anton Alekseev and Charles Torossian, and others, recently constructed a whole family of Drinfel'd associators, interpolating between the KZ associator and the anti-KZ associator. The KZ associator has the peculiar property that every multiple zeta value (MZV) appears in some coefficient of the series. Hidekazu Furusho proved in 2011 that, in fact, any Drinfel'd associator defines an evaluation on the algebra of formal MZVs. Hence the Rossi-Willwacher family of Drinfel'd associators induces a family of algebra morphisms (over the rationals) from formal MZVs to, say, complex numbers. I will present a stream-lined, geometric and fully explicit way of writing down the Rossi-Willwacher associators (and hence also of writing down the associated evaluations on MZVs).