Vishnu Jejjala, 2019/05/20, 15h, Deep Learning the Hyperbolic Volume of a Knot

An important conjecture in knot theory relates the large-$N$, double scaling limit of the colored Jones polynomial $J_{K,N}(q)$ of a knot $K$ to the hyperbolic volume of the knot complement, Vol($K$). A less studied question is whether Vol($K$) can be recovered directly from the original Jones polynomial ($N=1$). In this report we use a deep neural network to approximate Vol($K$) from the Jones polynomial.