We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian
knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya …

We conjecturally extract the triply graded Khovanov–Rozansky homology of the (m, n) torus
knot from the unique finite-dimensional simple representation of the rational DAHA of type A …

We argue how to identify the supersymmetric quiver quantum mechanics description of BPS
states, which arise in string theory in brane systems representing knots. This leads to a …

Abstract BPS quivers for N=2\:SU(N) gauge theories are derived via geometric engineering
from derived categories of toric Calabi-Yau threefolds. While the outcome is in agreement of …

We prove that the generating functions for the one row/column colored HOMFLY‐PT
invariants of arborescent links are specializations of the generating functions of the motivic …

In this paper, we find and explore the correspondence between quivers, torus knots, and
combinatorics of counting paths. Our first result pertains to quiver representation theory—we …

We prove that the generating functions for the colored HOMFLY-PT polynomials of rational
links are specializations of the generating functions of the motivic Donaldson–Thomas …

Lectures on knot homology Page 146 Contemporary Mathematics Volume 680 , 2016 http://dx.
doi. org/10.1090/conm/680/13702 Lectures on knot homology Satoshi Nawata and Alexei …

Given a planar curve singularity, we prove a conjecture of Oblomkov–Shende, relating the
geometry of its Hilbert scheme of points to the HOMFLY polynomial of the associated …

The theory of DAHA-Jones polynomials is extended from torus knots to their arbitrary
iterations (for any reduced root systems and weights), which includes the polynomiality …