We consider the construction of refined Chern–Simons torus knot invariants by M. Aganagic
and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's …

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 …

If a knot is represented by an m‐strand braid, then HOMFLY polynomial in representation R
is a sum over characters in all representations Q∈ R⊗ m. Coefficients in this sum are traces …

A bstract The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-
Simons theory, possess an especially simple representation for torus knots, which begins …

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 …

A bstract Explicit answer is given for the HOMFLY polynomial of the figure eight knot 4 1 in
arbitrary symmetric representation R=[p]. It generalizes the old answers for p= 1 and 2 and …

We study the interaction between Fourier-Mukai transforms and perverse filtrations for a
certain class of dualizable abelian fibrations. Multiplicativity of the perverse filtration and the" …

We construct a categorification of the maximal commutative subalgebra of the type A Hecke
algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal …

We relate the mixed Hodge structure on the cohomology of open positroid varieties (in
particular, their Betti numbers over C and point counts over F q) to Khovanov–Rozansky …

We suggest a construction for the Quantum Groups–Jones polynomials of torus knots in
terms of the PBW theorem of double affine Hecke algebra (DAHA) for any root systems and …