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X-WR-CALNAME:Aleksey Zinger: \"From Gromov-Witten invariants to integer 
 counts \"
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LAST-MODIFIED:20080930T194936Z
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DURATION:PT1H
LOCATION:Math 520\, Columbia University
DTSTAMP:20080930T194743Z
UID:EE6BCFDB-AFB5-4052-9FDA-E3019A4CCDA0
SEQUENCE:7
URL;VALUE=URI:http://math.columbia.edu/~lipshitz/SGGT/
DTSTART;TZID=America/New_York:20081024T130000
SUMMARY:Aleksey Zinger: \"From Gromov-Witten invariants to integer count
 s \"
DESCRIPTION:Abstract: Gromov-Witten invariants of a compact symplectic m
 anifold are certain virtual counts of J-holomorphic curves. These ration
 al numbers are rarely integer\, but are generally believed to be related
  to some integer counts. In string theory\, these counts are known as in
 staton numbers and BPS states. The predictions of Aspinwall-Morrison and
  Gopakumar-Vafa for the existence of BPS states of Calabi-Yau 3-folds ar
 e extended by Pandharipande to all 3-folds\, by Klemm-Pandharipande to a
 ll Calabi-Yau varieties in genus 0 and Calabi-Yau 4-folds in genus 1\, a
 nd by Pandharipande and the speaker to Calabi-Yau 5-folds in genus 1. Th
 e last extension came as a bit of a surprise to some string theorists\, 
 who also feel that extensions to higher dimensions are impossible. The a
 im of this talk is to survey the known predictions\, indicating how they
  arise\, how the 6-dimensional case differs from low-dimensional cases\,
  and why they hold for Fano classes in 3-folds (symplectic manifolds of 
 real dimension 6).
ORGANIZER;CN="Robert Lipshitz":mailto:lipshitz@math.stanford.edu
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