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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Periods\, the meromorphic 3D-index and the Turaev-
-Viro invariant - Stavros Garoufalidis (Max Planck
Institute for Mathematics)
DTSTART;TZID=Europe/London:20220915T090000
DTEND;TZID=Europe/London:20220915T100000
UID:TALK178142AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178142
DESCRIPTION:The 3D-index of Dimofte--Gaiotto--Gukov is an inte
resting collection of $q$-series with integer coef
ficients parametrised by a pair of integers and as
sociated to a 3-manifold with torus boundary. In t
his talk we explain the structure of the asymptoti
c expansions of the 3D-index when $q=e^{2\\pi i\\t
au}$ and $\\tau$ tends to zero (to all orders and
with exponentially small terms included)\, and dis
cover two phenomena: (a) when $\\tau$ tends to zer
o on a ray near the positive real axis\, the horiz
ontal asymptotics of the meromorphic 3D-index matc
h to all orders with the asymptotics of the Turaev
--Viro invariant of a knot\, in particular explain
ing the Volume Conjecture of Chen--Yang from first
principles\, (b) when $\\tau \\to 0$ on the posit
ive imaginary axis\, the vertical asymptotics of t
he 3D-index involves periods of a plane curve (the
$A$-polynomial)\, as opposed to algebraic numbers
\, explaining some predictions of Hodgson--Kricker
--Siejakowski and leading to conjectural identitie
s between periods of the $A$-polynomial of a knot
and integrals of the Euler beta-function. Joint wo
rk with Campbell Wheeler.
LOCATION:No Room Required
CONTACT:
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