Ivan Cherednik - DAHA superpolynomials for iterated link
It will be mostly an introduction to our long paper with Ivan Danilenko on DAHA superpolynomials of (colored) torus iterated links. Connections with the HOMFLY-PT polynomials and the Khovanov-Rozansky stable reduced polynomials will be briefly discussed. The theory of the latter is mostly developed for uncolored knots, especially in the reduced setting. Also, DAHA superpolynomials satisfy the super-duality (a theorem) and have other remarkable symmetries, which are generally difficult to approach topologically. Though the most clarifying proof of the super-duality for algebraic links is via the so-called motivic superpolynomials of plane curve singularities, conjecturally coinciding with the DAHA ones. The super-duality becomes then the functional equation, a fundamental development, which may have physics implications. The motivic direction inspired the Riemann hypothesis for DAHA superpolynomials (to be touched a bit at the end), but it will be omitted in this talk. We will focus on the DAHA theory of colored iterated links, explaining the main steps and providing some examples.