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SUMMARY:On the HOMFLY invariant of algebraic knots - Vivek Shende\, Prince
 ton
DTSTART:20100126T160000Z
DTEND:20100126T170000Z
UID:TALK22665@talks.cam.ac.uk
CONTACT:Jake Rasmussen
DESCRIPTION:A complex plane curve singularity determines\, by taking the b
 oundary of a\nsmall neighborhood\, an iterated torus link in the three-sph
 ere. The\nalgebraic geometry of the singularity and the topology of the li
 nk are\nintimately related\; for instance\, Zariski showed that the series
  of blowups\nneeded to resolve the singularity carries data equivalent to 
 the isotopy\nclass of the link. More recently\, Campillo\, Delgado\, and G
 usein-Zade gave a\nformula equating the Alexander polynomial of the link t
 o a generating series\npopulated by Euler characteristics of spaces of fun
 ctions defined at the\nsingularity. I will state a conjectural generalizat
 ion of their formula: the\nHOMFLY invariant of the link of a plane curve s
 ingularity is a generating\nfunction of Euler characteristics of moduli sp
 aces of schemes supported at\nthe singularity. I will discuss the evidence
  for the conjecture\, and show\nthat it holds for torus knots. The talk pr
 esents joint work with Alexei\nOblomkov.\n
LOCATION:MR 4
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