Marko Stošić, Instituto Superior Técnico and CAMGSD
Rational and algebraic links and knots-quivers correspondence
I will start with a brief overview of knots-quivers correspondence, where colored HOMFLY-PT (or BPS) invariants of the knot are expressed as motivic Donaldson-Thomas invariants of a corresponding quiver.
This deep conjectural relationship already had some surprising applications.
In this talk I will focus on showing that the knots-quivers correspondence holds for rational links, as well as much larger class of arborescent links (algebraic links in the sense of Conway). This is done by extending the correspondence to tangles, and showing that the set of tangles satisfying tangles-quivers correspondence is closed under the tangle addition operation.
This talk is based on joint work with Paul Wedrich.