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SUMMARY:New Calabi-Yau Manifolds from Genetic Algorithms - Elli Heyes (Cit
 y\, University of London)
DTSTART:20231110T113000Z
DTEND:20231110T123000Z
UID:TALK201877@talks.cam.ac.uk
DESCRIPTION:Calabi-Yau manifolds can be obtained as hypersurfaces in toric
  varieties built from reflexive polytopes.&nbsp\;We generate reflexive pol
 ytopes in various dimensions using a genetic algorithm.&nbsp\;As a proof o
 f principle\, we demonstrate that our algorithm reproduces the full set of
  reflexive polytopes in two and three dimensions\, and in four dimensions 
 with a small number of vertices and points.&nbsp\;Motivated by this result
 \, we construct five-dimensional reflexive polytopes with the lowest numbe
 r of vertices and points.By calculating the normal form of the polytopes\,
  we establish that many of these are not in existing datasets and therefor
 e give rise to new Calabi--Yau four-folds.In some instances\, the Hodge nu
 mbers we compute are new as well.\nCo-authors: Per Berglund\,&nbsp\;Yang-H
 ui He\,&nbsp\;Edward Hirst\,&nbsp\;Vishnu Jejjala\,&nbsp\;Andre Lukas
LOCATION:External
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