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SUMMARY:Hilbert schemes of singular plane curves and HOMFLY homology of th
 eir links - Shende\, V (Princeton)
DTSTART:20110414T140000Z
DTEND:20110414T150000Z
UID:TALK30784@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Intersecting a plane curve with the boundary of a small ball a
 round one of its singularities yields a link in the 3-sphere. To any link 
 may be attached a triply graded vector space\, the HOMFLY homology. Taking
  its Euler characteristic with respect to a certain grading gives the HOMF
 LY polynomial\, which in turn specializes variously to the Alexander polyn
 omial\, the Jones polynomial\, and the other SU(n) knot polynomials. \n\nW
 e will present a conjecture recovering this invariant from moduli spaces a
 ttached to the singular curve. Specifically\, we form the Hilbert schemes 
 of points of the curve\, and certain incidence varieties inside products o
 f Hilbert schemes. Up to certain shifts of grading\, we conjecture that th
 e HOMFLY homology of the link of the singularity is the direct sum of the 
 homologies of these spaces. \n\nThis talk presents joint work with J. Rasm
 ussen and A. Oblomkov. \n\n
LOCATION:Seminar Room 1\, Newton Institute
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