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CATEGORIES:Junior Geometry Seminar
SUMMARY:Skein algebra\, 3-manifolds and categorification -
Paul Wedrich (Imperial)
DTSTART;TZID=Europe/London:20170317T150000
DTEND;TZID=Europe/London:20170317T160000
UID:TALK69292AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/69292
DESCRIPTION:The Jones polynomial and its cousins are invariant
s of knots and links in the 3-sphere\, which are d
etermined by local so-called skein relations. This
allows a simple definition of an invariant of ori
ented 3-manifolds M: the space of all framed links
in M modulo the skein relations. Of particular in
terest are these invariants for thickened surfaces
\, in which case they carry an algebra structure a
nd act on the invariants of 3-manifolds co-boundin
g the surface. They are also related to character
varieties\, quantum Teichmueller spaces and featur
e in several important conjectures in quantum topo
logy. After surveying this area\, I will talk abou
t positive bases for skein algebras that were foun
d by D. Thurston\, and how they might be related t
o Khovanov's categorification of the Jones polynom
ial and its desired extension to a 4-dimensional T
QFT.
LOCATION:MR13
CONTACT:
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