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20/01/2011, 17:00 — 18:00 — Amphitheatre Pa1, Mathematics Building

Philip Candelas, *Mathematical Institute, University of Oxford*

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Periods of Calabi-Yau Manifolds in Physics and Number Theory

Calabi-Yau manifolds have many remarkable properties owing to their relation to string theory and supersymmetry. Every CY manifold has a holomorphic three-form and the integrals of this three form over a basis of three-cycles yield the periods of the manifold. The aim of the talk is to explain why two separate communities think that they "own" the periods. Physicists require the periods to calculate quantities pertaining to elementary particle interactions and number theorists know that the periods contain important arithmetic information about the manifold.