English

Abstract:
In this talk, I would like to expose current situation of the volume conjecture. This conjecture gives a relation on a knot between the volume of its complement and its quantum invariants. Such astonishing relation was first discovered by R. M. Kashaev for several hyperbolic knots, and many evidences were given after that. Especially, Y. Yokota showed an actual relation between the volume conjecture and the hyperbolic structure, which is a good approval for the conjecture. A quick review for knot complement case is given, and generalization to 3-manifolds is also discussed.