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SUMMARY:The Alexander polynomial as a Reshetikhin-Turaev invariant - Jonat
 han Grant (Durham)
DTSTART:20150306T150000Z
DTEND:20150306T160000Z
UID:TALK58384@talks.cam.ac.uk
CONTACT:Joe Waldron
DESCRIPTION:The Alexander polynomial is a classical invariant of knots int
 roduced in the 1920's with clear connections to the topology of knots and 
 surfaces. The Reshetikhin-Turaev invariants are much more recent\, and are
  in general much more poorly understood. These often arise from the repres
 entation theory of quantum groups. I will show how the Alexander polynomia
 l can be interpreted\nas a Reshetikhin-Turaev invariant using representati
 ons of U_q(gl(1|1))\, and show how this can be used to understand a catego
 ry of representations of\nU_q(gl(1|1)). Finally\, I will explain how this 
 relates to the theory of highest weight modules of U_q(gl(m))\, and can be
  categorified using projective modules over cyclotomic KLR algebras\, and 
 how the theory of foams\nfor sl_n knot homology fit into this picture.
LOCATION:MR13
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