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SUMMARY:DAHA superpolynomials of torus knots
DTSTART:20141027T151500
DTEND:20141027T170000
DTSTAMP:20260510T235205Z
UID:39694cfaa037d2b0063c306e2271a86efb81170fb5a39d5111dc26d5
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ivan Cherednik (UNC-Chapel Hill)\nI will define the DAHA-Jones
  (refined) polynomials of torus knots\nfor any root systems and any weight
 s (practically from scratch).\nThey generalize the Jones-WRT invariants ba
 sed on Quantum Groups\;\nthe coincidence was checked for types A-C by now.
  In type A\,\nthe DAHA-Jones polynomials for all A_n can be combined in on
 e\nsingle DAHA-superpolynomial\, presumably coinciding with the stable\nKh
 ovanov-Rozansky polynomial for sl(N) of the corresponding torus\nknot and 
 with that obtained from the BPS states in the M5 theory\n(String Theory). 
 The DAHA-superpolynomials match very well\nsuperpolynomials obtained via p
 erfect modules of rational DAHA\n(Gorsky\, Oblomkov\, Rasmussen\, Shende) 
 and related to Hilbert\nschemes of singular plane curves\; the approach vi
 a rational\nDAHA will be touched upon a little. If time permits\, I will s
 ay\nsomething about my recent papers\; the latest (with I. Danilenko)\next
 ends the above theory to iterated torus knots and establishes\na deep (con
 jectural) connection of the DAHA-superpolynomials\nwith the geometry of (a
 ny) unibranch plane curve singularities.\nThis is related to the Oblomkov-
 Rasmussen-Shende conjecture\,\ngeneralizing the Oblomkov-Shende conjecture
  proved by Maulik.
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STATUS:CONFIRMED
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