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SUMMARY:Integrality of relative BPS state counts of toric Del Pezzo surfac
 es
DTSTART:20140117T130000
DTEND:20140117T140000
DTSTAMP:20260428T043917Z
UID:7485387d7134f29c3a091cbf75c042e3b926852cd8e2f4dab8732b65
CATEGORIES:Conferences - Seminars
DESCRIPTION:Michel van Garrel (University of Alberta)\nAbstract :\nRelativ
 e BPS state counts for log Calabi-Yau surface pairs were introduced by Gro
 ss-Pandharipande-Siebert and conjectured by the authors to be integers. Fo
 r toric Del Pezzo surfaces\, we provide an arithmetic proof of this conjec
 ture\, by relating these invariants to the local BPS state counts of the s
 urfaces. The latter were shown to be integers by Peng\; and more generally
  for toric Calabi-Yau threefolds by Konishi. Local BPS state counts were c
 omputed by Chiang-Klemm-Yau-Zaslow via local mirror symmetry. Analogously\
 , relative BPS state counts are related to log mirror symmetry\, which for
  the projective plane was developed by Takahashi. Relative BPS state count
 s are an intrinsic (virtual) extension of the A-model invariants considere
 d by Takahashi. The relative BPS state counts satisfy an adapted log mirro
 r symmetry conjecture by Takahashi: they are linearly related to the local
  BPS state counts and are thus calculated by periods of the mirror family.
LOCATION:MA30 http://plan.epfl.ch/?room=MA%20A3%2030
STATUS:CONFIRMED
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