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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Speaker: Ka Ho Wong (Yale University)\n\nTitle: Asymptotics o
f the relative Reshetikhin-Turaev invariants\n\nAbstract: In a series of j
oint works with Tian Yang\, we made a volume conjecture and an asymptotic e
xpansion conjecture for the relative Reshetikhin-Turaev invariants of a clo
sed oriented 3-manifold with a colored framed link inside it. We propose th
at their asymptotic behavior is related to the volume\, the Chern-Simons in
variant and the adjoint twisted Reidemeister torsion associated with the hy
perbolic cone metric on the manifold with singular locus the link and cone
angles determined by the coloring.\n\nIn this talk\, I will first discuss h
ow our volume conjecture can be understood as an interpolation between the
Kashaev-Murakami-Murakami volume conjecture of the colored Jones polynomial
s and the Chen-Yang volume conjecture of the Reshetikhin-Turaev invariants.
Then I will describe how the adjoint twisted Reidemeister torsion shows up
in the asymptotic expansion of the invariants. Especially\, we find new ex
plicit formulas for the adjoint twisted Reidemeister torsion of the fundame
ntal shadow link complements and of the 3-manifolds obtained by doing hyper
bolic Dehn-filling on those link complements. Those formulas cover a very l
arge class of hyperbolic 3-manifolds and appear naturally in the asymptotic
expansion of quantum invariants. Finally\, I will discuss some recent prog
ress of the asymptotic expansion conjecture of the fundamental shadow link
pairs.
DTEND:20231120T210000Z
DTSTAMP:20240415T160716Z
DTSTART:20231120T200000Z
LOCATION:Building 2\, 2-449
SEQUENCE:0
SUMMARY:MIT Geometry and Topology Seminar
UID:tag:localist.com\,2008:EventInstance_44280022659431
URL:https://calendar.mit.edu/event/mit_geometry_and_topology_seminar_3345
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