Geometry and Topology Seminar: Multivariable knot polynomials, the V_n-polynomials, and their patterns

Speaker: Shana Yunsheng Li from University of Illinois at Urbana-Champaign
Host: Xiaolong Hans Han

Abstract: Quantum knot invariants are known to come from R-matrices along with some extra structures, a process called the Reshetikhin–Turaev functor. In , Rinat Kashaev proved that R-matrices alone 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 results based on 361404 knots computed. Joint work with Stavros Garoufalidis.

Time: 04/24, Thursday, 9 am
Location: Zoom Meeting ID: 953 6121 6208 (passcode: 025815)