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SUMMARY:Hopf-algebraic Renormalization of Multiple Zeta Values and their q
-analogues
DTSTART;VALUE=DATE-TIME:20201117T123000Z
DTEND;VALUE=DATE-TIME:20201117T132000Z
DTSTAMP;VALUE=DATE-TIME:20210508T034607Z
UID:indico-contribution-4761@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dominique MANCHON (CNRS & Université Clermont-Auver
gne)\nMultiple zeta values are real numbers which appeared in depth one an
d two in the work of L. Euler in the Eighteenth century. They first appear
as a whole in the work of J. Ecalle in 1981\, as infinite nested sums. A
systematic study starts one decade later with M. Hoffman\, D. Zagier and M
. Kontsevich\, with multiple polylogarithms and iterated integral represen
tation as a main tool. After a brief historical account\, I'll explain how
a quasi-shuffle compatible definition (by no means unique) can be given t
hrough Connes-Kreimer's Hopf-algebraic renormalization when the nested sum
diverges. I'll also give an account of the more delicate renormalization
of shuffle relations. Finally\, I'll introduce the Ohno-Okuda-Zudilin mode
l of q-analogues for multiple zeta values\, and describe the algebraic str
ucture which governs it.\n\nhttps://indico.math.cnrs.fr/event/4834/contrib
utions/4761/
LOCATION:IHES Marilyn and James Simons Conference Center
URL:https://indico.math.cnrs.fr/event/4834/contributions/4761/
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