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15 mars 2018: 1 événement

  • Colloquium

    Jeudi 15 mars 16:30-17:30 - Rei Inoue - Chiba University, Japan

    Cluster braiding operator and volume of knots

    Résumé : The cluster algebra was introduced by Fomin and Zelevinsky around 2000.
    The characteristic operation in the algebra called "mutation" is related to various notions in mathematics and mathematical physics.
    In this talk I introduce the basic notion of mutation and its application to study volume of knots.
    In three-dimensional hyperbolic geometry, a mutation is interpreted to produce an ideal tetrahedron,and cluster y-variables are regarded as the modulus of ideal tetrahedra. We define the octahedral braiding operator (R-operator) composed of four mutations, and study the volume of knot complements in S^3. Further, by using the quantum cluster algebra a la Fock and Goncharov, we quantize the R-operator, and discuss "the volume conjecture" of knot,from the view point of cluster algebra.
    This talk is based on joint work with Kazuhiro Hikami.

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