Tran, Anh T.

 

Anh Tran is an Associate Professor of Mathematics. His research interests are focused on quantum topology and knot theory especially as they relate to the Jones polynomial, skein modules, charactyer varieties, the A-polynomial, the Alexander polynomial, and left-orderability of fundamental groups.

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Recent Submissions

  • Left-Orderability for Surgeries on Twisted Torus Knots 

    Tran, Anh T. (Japan Academy, 2019-01)
    We show that the fundamental group of the 3-manifold obtained by p/q-surgery along the (n - 2)-twisted (3, 3m + 2)-torus knot, with n, m ≥ 1, is not left-orderable if p/q ≥ 2n + 6m - 3 and is left-orderable if p/q is ...

  • The Asymptotics of the Higher Dimensional Reidemeister Torsion for Exceptional Surgeries Along Twist Knots 

    Tran, Anh T.; Yamaguchi, Yoshikazu
    We determine the asymptotic behavior of the higher dimensional Reidemeister torsion for the graph manifolds obtained by exceptional surgeries along twist knots. We show that all irreducible SL2

  • On the AJ Conjecture for Knots 

    Le, Thang T. Q.; Tran, Anh T.; Huynh, Vu Q. (2015-07-07)
    We confirm the AJ conjecture [Ga2] that relates the A-polynomial and the colored Jones polynomial for hyperbolic knots satisfying certain conditions. In particular, we show that the conjecture holds true for some classes ...

  • Knot Cabling and the Degree of the Colored Jones Polynomial 

    Kalfagianni, E.; Tran, Anh T. (University at Albany, 2015-09-16)
    We study the behavior of the degree of the colored Jones polynomial and the boundary slopes of knots under the operation of cabling. We show that, under certain hypothesis on this degree, if a knot K satisfies the Slope ...