Knots and quivers, HOMFLYPT and DT

Abstract: I will describe a surprising connection between the colored HOMFLY-PT polynomials of knots and the motivic Donaldson-Thomas invariants of certain symmetric quivers, which was conjectured by Kucharski-Reineke-Stosic-Sulkowski. I will outline a proof of this correspondence for arborescent links via quivers associated with 4-ended tangles. Finally, I will speculate about how much of the HOMFLY-PT skein theory might carry over to the realm of DT quiver invariants and what kind of geometric information about knots might be encoded in these quivers. This is joint work with Marko Stosic.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.