Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

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

Event Type: Seminar/Symposium
Sponsor: Groups, Geometry, and Topology Seminar
Location: 347 Altgeld Hall
Date: Sep 11, 2025 11:00 am - 12:00 pm
Speaker: Shana Li (Illinois)
Views: 27
Originating Calendar: Groups, Geometry, and Topology Calendar; 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.

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