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SUMMARY:Moduli spaces of discs and multiple zeta values in deformation qua
ntization
DTSTART;VALUE=DATE-TIME:20181213T153000Z
DTEND;VALUE=DATE-TIME:20181213T163000Z
DTSTAMP;VALUE=DATE-TIME:20200716T143658Z
UID:indico-event-4240@indico.math.cnrs.fr
DESCRIPTION:Kontsevich's 1997 proof of the formality conjecture provides a
universal quantization of every Poisson manifold\, by a formal power seri
es whose coefficients are integrals over moduli spaces of marked discs. In
joint work with Peter Banks and Brent Pym\, we prove that these integrals
evaluate to multiple zeta values\, which are interesting transcendental n
umbers known from the Drinfeld associator and as the periods of mixed Tate
motives. Our proof is algorithmic and allows for the explicit computation
of arbitrary coefficients in the formality morphism\, in particular the s
tar product. The essential tools are Francis Brown's theory of polylogarit
hms on the moduli space of marked genus zero curves\, single-valued integr
ation due to Oliver Schnetz\, and an induction over the natural fibrations
of moduli spaces.\n\nhttps://indico.math.cnrs.fr/event/4240/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4240/
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