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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Gamma functions\, monodromy and Ap&\;eacute\;ry
constants - Masha Vlasenko (Polish Academy of Sci
ences)
DTSTART;TZID=Europe/London:20200127T150000
DTEND;TZID=Europe/London:20200127T160000
UID:TALK138391AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/138391
DESCRIPTION:In their paper on the gamma conjecture in mirror s
ymmetry\, Golyshev and Zagier introduce a sequence
of Apé\;ry constants associated to an ordin
ary linear differential operator with a choice of
two singular points and a path between them. Their
setting also involves assumptions on the local mo
nodromies around the two points (maximally unipote
nt and reflection point respectively). In particul
ar\, these assumptions are satisfied in the situat
ion of Apé\;ry'\;s proof of irrationality
of zeta(3)\, and in this case Golyshev and Zagier
discover that (numerically\, with high precision)
the higher constants in the sequence seem to be r
ational linear combinations of weighted products o
f zeta and multiple zeta values. In the joint work
with Spencer Bloch we show that\, quite generally
\, the generating series of Apé\;ry constant
s is a Mellin transform of a solution of the adjoi
nt differential operator. This peculiar property e
xplains why Apé\;ry constants of geometric d
ifferential operators are periods\, which seems to
be the first step in the study of their motivic n
ature.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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