DAHA superpolynomials of torus knots
Event details
| Date | 27.10.2014 |
| Hour | 15:15 › 17:00 |
| Speaker | Ivan Cherednik (UNC-Chapel Hill) |
| Location | |
| Category | Conferences - Seminars |
I will define the DAHA-Jones (refined) polynomials of torus knots
for any root systems and any weights (practically from scratch).
They generalize the Jones-WRT invariants based on Quantum Groups;
the coincidence was checked for types A-C by now. In type A,
the DAHA-Jones polynomials for all A_n can be combined in one
single DAHA-superpolynomial, presumably coinciding with the stable
Khovanov-Rozansky polynomial for sl(N) of the corresponding torus
knot and with that obtained from the BPS states in the M5 theory
(String Theory). The DAHA-superpolynomials match very well
superpolynomials obtained via perfect modules of rational DAHA
(Gorsky, Oblomkov, Rasmussen, Shende) and related to Hilbert
schemes of singular plane curves; the approach via rational
DAHA will be touched upon a little. If time permits, I will say
something about my recent papers; the latest (with I. Danilenko)
extends the above theory to iterated torus knots and establishes
a deep (conjectural) connection of the DAHA-superpolynomials
with the geometry of (any) unibranch plane curve singularities.
This is related to the Oblomkov-Rasmussen-Shende conjecture,
generalizing the Oblomkov-Shende conjecture proved by Maulik.
for any root systems and any weights (practically from scratch).
They generalize the Jones-WRT invariants based on Quantum Groups;
the coincidence was checked for types A-C by now. In type A,
the DAHA-Jones polynomials for all A_n can be combined in one
single DAHA-superpolynomial, presumably coinciding with the stable
Khovanov-Rozansky polynomial for sl(N) of the corresponding torus
knot and with that obtained from the BPS states in the M5 theory
(String Theory). The DAHA-superpolynomials match very well
superpolynomials obtained via perfect modules of rational DAHA
(Gorsky, Oblomkov, Rasmussen, Shende) and related to Hilbert
schemes of singular plane curves; the approach via rational
DAHA will be touched upon a little. If time permits, I will say
something about my recent papers; the latest (with I. Danilenko)
extends the above theory to iterated torus knots and establishes
a deep (conjectural) connection of the DAHA-superpolynomials
with the geometry of (any) unibranch plane curve singularities.
This is related to the Oblomkov-Rasmussen-Shende conjecture,
generalizing the Oblomkov-Shende conjecture proved by Maulik.
Practical information
- General public
- Free