  We report on the observation of confinement-induced resonances in strongly
interacting quantum-gas systems with tunable interactions for one- and
two-dimensional geometry. Atom-atom scattering is substantially modified when
the s-wave scattering length approaches the length scale associated with the
tight transversal confinement, leading to characteristic loss and heating
signatures. Upon introducing an anisotropy for the transversal confinement we
observe a splitting of the confinement-induced resonance. With increasing
anisotropy additional resonances appear. In the limit of a two-dimensional
system we find that one resonance persists.
