Odd Khovanov homology and higher representation theory

Abstract: Khovanov homology is a homological invariant of links categorifying the Jones polynomial. It is by now well-understood through the lens of higher representation theory, categorifying the relationship between the Jones polynomial and the representation theory of Uq(sl2). Surprisingly, there exists another categorification of the Jones polynomial, called odd Khovanov homology. Subsequently, higher odd (or “super”) analogues were discovered in representation theoretic and geometric contexts. In this talk, I will begin with a gentle introduction to the above, and then explain how odd Khovanov homology can be understood as stemming from a supercategorification of the representation theory of Uq(gl2). This is joint work with Pedro Vaz.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home