DAHA approach to algebraic knots and links

DAHA generally provide refined invariants of colored iterated links, which generalize the
WRT-invariants and HOMFLY-PT polynomials. In the uncolored case and for iterated knots,
they are conjectured to coincide with the stable reduced Khovanov-Rozansky polynomials (the most
powerful numerical invariants we have). The "intrinsic" DAHA conjectures are mostly verified
at the moment; these properties are generally difficult to check topologically. The DAHA super-
duality is an important example (a theorem for DAHA, but far from obvious in topology).
Its conjectural coincidence with the functional equation in the motivic approach (my next talk),
can be a fundamental development.  We will focus on the DAHA construction in this talk, with
some explicit calculations (for trefoil and beyond).