**Philip Candelas**

Oxford University

March 15, 2011

** Periods of Calabi-Yau Manifolds in Physics and Number Theory**:
A Calabi-Yau manifold has a naturally defined holomorphic three-form
and the integrals of this over a basis of homology cycles are the
periods of the manifold. These periods depend on the complex structure
parameters. It transpires that there are two communities that think
they own the periods. String theorists compute quantities to do with
the effective four dimensional theory and these are usually computed
in terms of the periods. Number theorists also regard the periods as
their own, since they encode important arithmetic information about
the manifold. I will show how the number of F_p - rational points is
calculated in terms of the periods and comment about the form of the
zeta-function and its relation to mirror symmetry.