Séminaires : Groupes, Représentations et Géométrie

Equipe(s) : gr,
Responsables :Adrien Brochier, Olivier Brunat, Jean-Yves Charbonnel, Olivier Dudas, Daniel Juteau, Emmanuel Letellier, Michela Varagnolo, Eric Vasserot
Email des responsables : adrien.brochier@imj-prg.fr ; olivier.brunat@imj-prg.fr; jean-yves.charbonnel@imj-prg.fr; olivier.dudas@imj-prg.fr; emmanuel.letellier@imj-prg.fr; daniel.juteau@imj-prg.fr; varagnol@math.u-cergy.fr; eric.vasserot@imj-prg.fr
Salle : 1016
Adresse :Sophie Germain

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Orateur(s) Jennifer Brown - ,
Titre Skein Theory and Quantized Knot Invariants
Horaire10:30 à 12:15
Skein theory gives both a method of producing knot invariants and a way to quantize character varieties of surfaces and the three manifolds they bound. There is a well supported but conjectural relationship between these two aspects of skeins -- that the character variety of a knot complement is determined in a specific way by the invariant of the corresponding knot. This is known as the AJ conjecture, because it was originally formulated as a relationship between two knot invariants known as the A-polynomial and the colored Jones polynomial. A missing ingredient in this conjecture is a concrete and general procedure for computing the quantized character variety of a knot complement, i.e. quantizing the A-polynomial.
The first half of this walk will be a friendly introduction to skein categories, algebras, and modules. The second half will introduce character varieties, explain their quantization by skein algebras, and discuss how this relates to the AJ conjecture.
AdresseSophie Germain