GGT seminar: Multivariable knot polynomials, the V_n-polynomials, and their patterns.

Quantum knot invariants are known to come from R-matrices along with some extra structures, a process called the Reshetikhin--Turaev functor. In 2019, Rinat Kashaev proved that R-matrices are sufficient to define knot invariants, as long as they satisfy some nondegeneracy conditions called rigidity. More recently, Stavros Garoufalidis and Rinat Kashaev developed a new method of constructing rigid R-matrices, which recovers several known knot polynomials such as the colored Jones polynomials, and gives a new family of multivariable knot polynomials, the V_n-polynomials. In this talk, I will talk about the Reshetikhin--Turaev functor in this context, the computation of V_n-polynomials and the patterns of the V_2-polynomial based on the 1,701,935 knots computed. Joint work with Stavros Garoufalidis.