Using Hecke algebras and Verlinde algebras for calculating the Jones and
HOMFLYPT polynomials of torus knots is generally well understood, though
the explicit formulas attract a lot of attention even for the simplest knots and
are used in the theory of A-polynomials as well as in Number Theory. I will
define the DAHA-Jones (refined) polynomials of torus knots for any root
systems and any weights (practically from scratch). They generalize those
based on Quantum Groups, which was checked for types A-C-D by now.
In type A, the DAHA-superpolynomials will be introduced, presumably
coinciding with the stable Khovanov-Rozansky polynomials for sl(N) and
with those obtained via the BPS states in the M5 theory (String Theory).
If time permits, type C will be briefly dicussed, including some latest
developments in the rank one case