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SUMMARY:An AJ conjecture for trivalent graphs
DTSTART:20261002T120000Z
DTEND:20261002T130000Z
DTSTAMP:20260930T200100Z
UID:indico-event-17355@indico.math.cnrs.fr
CONTACT:kellendonk@math.univ-lyon1.fr\;athomas@math.univ-lyon1.fr
DESCRIPTION:Speakers: Ramanujan Santharoubane (Orsay)\n\nThe coloured Jone
 s polynomial is a sequence of Laurent polynomials associated with a knot. 
 In 2003\, Garoufalidis and Lê proved that the coloured Jones polynomial o
 f a given knot satisfies a kind of recurrence relation\, called aq-differe
 nce equation. One year later\, Garoufalidis proposed a conjecture\, now kn
 own as the AJ conjecture\, stating that a certain evaluation of this q-dif
 ference equation recovers the A-polynomial of the knot. The A-polynomial i
 s an important classical invariant: a two-variable Laurent polynomial that
  encodes the restriction map from the SL(2\,C) character variety of the kn
 ot exterior to that of its boundary torus.\nIn this talk I will explain ho
 w to generalise this conjecture to embeddings of trivalent graphs in the 3
 -sphere\, replacing the coloured Jones polynomial by the coloured Kauffman
  bracket of the graph. This generalisation recovers the original conjectur
 e\, and we will see that for planar embeddings the new conjecture holds.\n
 This is joint work in progress with Renaud Detcherry and Louis Ioos.\n\nht
 tps://indico.math.cnrs.fr/event/17355/
LOCATION:Salle Fokko du Cloux (Bat. Braconnier)
URL:https://indico.math.cnrs.fr/event/17355/
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