CCMS Colloquium: Stable Khovanov Homology for Torus Links — Christine Lee (Texas State University)

Abstract: Stable Khovanov homology \(Kh(T(n, \infty))\) is an algebraic limit of the Khovanov homology groups of torus links \(T(n, k) \) on a fixed number of strands \(n\), when more and more full twists are added as \(k \to \infty\). Stable Khovanov homology is intimately related to the Jones polynomial because it categorifies the Jones-Wenzl projector, which can be used to define the colored Jones polynomial.

We still do not completely understand \(Kh(T(n, \infty))\). The Gorsky-Oblomkov-Rasmussen conjecture predicts a simple form of the complex for which the explicit forms of the differentials are still open. I will talk about my summer research project with a group of undergraduate students where we use a process called “whittling” to compute explicit forms of the differentials for 3- and 4-stranded torus braids. We expect our results will serve as the base case for an induction proof of the GOR conjecture.

Besides the discussion on providing meaningful research experience for undergraduate students, the computational aspects of the project may be of interest to the audience. The students were organized into a “math” team and a “computer” team to encourage interaction of these perspectives in pursuit of a common goal.

For questions about the event, please contact your CCMS Colloquium chairs:

Prof. Robert Cass (Robert.Cass@ClaremontMcKenna.edu) or Prof. Qidi Peng (Qidi.Peng@cgu.edu)

For logistical questions, contact Maxwell Kooiker (Maxwell.Kooiker@cgu.edu), the CCMS Colloquium Assistant.