  We explore the effects of collective neutrino flavor oscillations due to
neutrino-neutrino interactions on the neutrino heating behind a stalled
core-collapse supernova shock. We carry out axisymmetric (2D)
radiation-hydrodynamic core-collapse supernova simulations, tracking the first
400 ms of the post-core-bounce evolution in 11.2 solar mass and 15 solar mass
progenitor stars. Using inputs from these 2D simulations, we perform neutrino
flavor oscillation calculations in multi-energy single-angle and multi-angle
single-energy approximations. Our results show that flavor conversions do not
set in until close to or outside the stalled shock, enhancing heating by not
more than a few percent in the most optimistic case. Consequently, we conclude
that the postbounce pre-explosion dynamics of standard core-collapse supernovae
remains unaffected by neutrino oscillations. Multi-angle effects in regions of
high electron density can further inhibit collective oscillations,
strengthening our conclusion.
