6 papers
The knot polynomial
Stavros Garoufalidis, Shana Yunsheng Li
We present the knot polynomial associated to the 12-dimensional sporadic Nichols algebra with automorphism, compute it for all knots with 16 crossings and di…
Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networks
Shana Yunsheng Li
We give a thorough analysis of the time complexity of computing Reshetikhin--Turaev knot polynomials via tensor contractions on the associated tensor networks, showing that the com…
Positivity and log concavity of the Links--Gould polynomial of knots
Stavros Garoufalidis, Shana Yunsheng Li, Josephine Yu
Motivated by the recent work of Harper--Kohli--Song--Tahar, we formulate a positivity, hole-free, and log-concavity conjecture for the Links--Gould polynomial of alternating links…
The complete -tetrahedra census of orientable cusped hyperbolic -manifolds
Shana Yunsheng Li
We extend the complete census of orientable cusped hyperbolic -manifolds to tetrahedra, giving the next manifolds and their minimal ideal triangulations.…
Patterns of the -polynomial of knots
Stavros Garoufalidis, Shana Yunsheng Li
Recently, Kashaev and the first author constructed an -matrix from a Nichols algebra with an automorphism, that leads, via the Reshetikhin--Turaev functor, to a multivariable po…
Algebraic aspects of holomorphic quantum modular forms
Ni An, Stavros Garoufalidis, Shana Yunsheng Li
Matrix-valued holomorphic quantum modular forms are intricate objects that arise in successive refinements of the Volume Conjecture of knots and involve three holomorphic, asymptot…