  Theories with large extra dimensions may be tested using sterile neutrinos
living in the bulk. A bulk neutrino can mix with a flavor neutrino localized in
the brane leading to unconventional patterns of neutrino oscillations. A
resonance phenomenon, strong mixing between the flavor and the sterile
neutrino, allows to determine the radius of the large extra dimension. If our
brane is curved, then the sterile neutrino can take a shortcut through the
bulk, leading to an apparent superluminal neutrino speed. The amount of
"superluminality" is directly connected to parameters determining the shape of
the brane. On the experimental side, we suggest that a long baseline neutrino
beam from CERN to NESTOR neutrino telescope will help to clarify these
important issues.
