Orateur: Quingtao Chen (ETH Zurich)
Titre: Quantum invariants, Skein relations and Volume conjecture.
Résumé:  In knot theory, Jones, HOMFLY and Kauffman polynomials share a common feature that they can be defined via a purely combinatorial method called skein relation. But it's rather hard to search skein relations for quantum invariants. Recently, we proposed several conjectures of congruent skein relations for colored HOMFLY invariants and colored Jones polynomials etc. We have proved series of examples for these new conjectures. The motivation behind this phenomenon involves several areas of mathematics as well as string theory, which may also shed some new light on the Volume conjecture. This is a joint work with Kefeng Liu, Pan Peng and Shengmao Zhu. Finally I will introduce a very recent discovery of Volume Conjectures for hyperbolic 3-manifolds through Turaev-Viro type invariants and Reshetikhin-Turaev invariants evaluated at roots of unity other than the usual root of unity considered by Witten.

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