Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Deformation quantization, moduli spaces of discs and multiple zeta values

Kontsevich's 1997 proof of the formality conjecture provides a universal quantization of every Poisson manifold, by a formal power series whose coefficients are integrals over moduli spaces of marked discs. In joint work with Peter Banks and Brent Pym, we proved that these integrals evaluate to multiple zeta values, which are interesting transcendental numbers known from the Drinfeld associator and as the periods of mixed Tate motives. Our proof is algorithmic and allows for the explicit computation of the coefficients in the formality morphism, in particular the star product. The essential tools are Francis Brown's theory of polylogarithms on the moduli space of marked genus zero curves, single-valued integration due to Oliver Schnetz, and an induction over the natural fibrations of moduli spaces.