  These are lecture notes for two lectures delivered at the Les Houches
workshop on Number Theory, Physics, and Geometry, March 2003. They review two
examples of interesting interactions between number theory and string
compactification, and raise some new questions and issues in the context of
those examples. The first example concerns the role of the Rademacher expansion
of coefficients of modular forms in the AdS/CFT correspondence. The second
example concerns the role of the ``attractor mechanism'' of supergravity in
selecting certain arithmetic Calabi-Yau's as distinguished compactifications.
