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SUMMARY:Integrality of instanton numbers - Masha Vlasenko (Polish Academy 
 of Sciences)
DTSTART:20220722T080000Z
DTEND:20220722T090000Z
UID:TALK175046@talks.cam.ac.uk
DESCRIPTION:Instanton numbers of Calabi--Yau threefolds are defined by Gro
 mov--Witten theory. They 'count' curves of fixed degree on the manifold. T
 he actual definition involves integration over the moduli space of curves\
 , which gives a priori rational numbers. The mirror theorem allows one to 
 express them in terms of solutions of a differential equation on the mirro
 r manifold. However\, the integrality of instanton numbers is not clear fr
 om this expression either. In 2003 Jan Stienstra outlined an approach to i
 ntegrality using the p-adic Frobenius structure on the differential equati
 on. In a recent series of papers with Frits Beukers we propose an explicit
  and rather elementary construction of the Frobenius structure\, which all
 ows us to prove integrality of instanton numbers in several key examples o
 f mirror symmetry. In this talk I will speak about the beginnings of mirro
 r symmetry and explain the ideas of our construction.
LOCATION:Seminar Room 1\, Newton Institute
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