Ivan Danilenko (Columbia), DAHA and iterated torus links


Jones polynomials and WRT invariants are well-known invariants of links in S^3. Their categorification attracts a lot of attention now. The key numerical invariant here is the Poincare polynomial of the triply graded Khovanov-Rozansky homology, also called HOMFLYPT homology. In spite of recent developments, this theory remains very difficult apart from the celebrated Khovanov homology (the case of sl(2)) with very few known formulas (only for the simplest uncolored knots). Several alternative approaches to these polynomials were suggested recently (the connections are mostly conjectural). We will discuss the direction based on DAHA, which was recently extended from torus knots to arbitrary torus iterated links (including all algebraic links). The talk will be mostly focused on the DAHA-Jones polynomial of type A_1, which is essentially sufficient to understand the procedures we employ and to see which steps are needed to go from torus knots to arbitrary iterated knots/links. Based on our joint works with Ivan Cherednik.