University of Sydney Algebra Seminar

Hoel Queffelec (ANU)

Friday 10 October, 12:05-12:55pm, Place: 373

Foam categories from categorified quantum groups

About 15 years ago, Khovanov introduced a homological invariant of knots categoryfying the Jones polynomial. Though this polynomial can be viewed both from a representation-theoretic and a diagrammatic point of view, for long only the latter version has been categorified. I will explain how, using the concept of skew-Howe duality developed by Cautis, Kamnitzer, Morrison and Licata, one can describe the cobordism categories used in Khovanov homology from the point of view of categorified quantum groups. One can in turn use these categorified quantum groups to precisely define sln-generalizations of the cobordism categories, allowing for a complete combinatorial and integral definition of Khovanov-Rozansky homologies. This is joint work with Aaron Lauda and David Rose.