BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Periods\, the meromorphic 3D-index and the Turaev--Viro invariant 
 - Stavros Garoufalidis (Max Planck Institute for Mathematics)
DTSTART:20220915T080000Z
DTEND:20220915T090000Z
UID:TALK178142@talks.cam.ac.uk
DESCRIPTION:The 3D-index of Dimofte--Gaiotto--Gukov is an interesting coll
 ection of $q$-series with integer coefficients parametrised by a pair of i
 ntegers and associated to a 3-manifold with torus boundary. In this talk w
 e explain the structure of the asymptotic expansions of the 3D-index when 
 $q=e^{2\\pi i\\tau}$ and $\\tau$ tends to zero (to all orders and with exp
 onentially small terms included)\, and discover two phenomena: (a) when $\
 \tau$ tends to zero on a ray near the positive real axis\, the horizontal 
 asymptotics of the meromorphic 3D-index match to all orders with the asymp
 totics of the Turaev--Viro invariant of a knot\, in particular explaining 
 the Volume Conjecture of Chen--Yang from first principles\, (b) when $\\ta
 u \\to 0$ on the positive imaginary axis\, the vertical asymptotics of the
  3D-index involves periods of a plane curve (the $A$-polynomial)\, as oppo
 sed to algebraic numbers\, explaining some predictions of Hodgson--Kricker
 --Siejakowski and leading to conjectural identities between periods of the
  $A$-polynomial of a knot and integrals of the Euler beta-function. Joint 
 work with Campbell Wheeler.
LOCATION:No Room Required
END:VEVENT
END:VCALENDAR