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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Differential equations and mixed Hodge structures
- Matt Kerr (Washington University in St. Louis)
DTSTART;TZID=Europe/London:20220621T150000
DTEND;TZID=Europe/London:20220621T160000
UID:TALK174416AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/174416
DESCRIPTION:We report on a new development in asymptotic Hodge
theory\, arising from work of Golyshev-Zagier and
Bloch-Vlasenko\, and connected to the Gamma Conje
ctures in Fano/LG-model mirror symmetry. \;Th
e talk will focus exclusively on the Hodge/period-
theoretic aspects.\n \; Given a variation of H
odge structure M on a Zariski open in P^1\, the pe
riods of the limiting mixed Hodge structures at th
e punctures are interesting invariants of M.
\;More generally\, one can try to compute these as
ymptotic invariants for iterated extensions of M b
y "Tate objects"\, which may arise for example fro
m normal functions associated to algebraic cycles.
\;\n \; The main point of the talk will
be that (with suitable assumptions on M) these inv
ariants are encoded in an entire function called t
he motivic Gamma function\, which is determined by
the Picard-Fuchs operator L underlying M. \;
In particular\, when L is hypergeometric\, this is
easy to compute and we get a closed-form answer (
and a limiting motive). \;\n \; Though th
at is probably enough for a single talk\, perhaps
one more thing is worth mentioning in this abstrac
t: \;in the next simplest class of cases beyo
nd hypergeometric\, the leading Taylor coefficient
of the motivic Gamma at 1 is given by the special
value of a normal function\, and in one special c
ase this recovers Apery&rsquo\;s irrationality pro
of for zeta(3).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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