  We study the phenomena of energy concentration for the critical O(3) sigma
model, also known as the wave map flow from R^{2+1} Minkowski space into the
sphere S^2. We establish rigorously and constructively existence of a set of
smooth initial data resulting in a dynamic finite time formation of
singularities. The construction and analysis is done in the context of the
k-equivariant symmetry reduction, and we restrict to maps with homotopy class
k>3. The concentration mechanism we uncover is essentially due to a resonant
self-focusing (shrinking) of a corresponding harmonic map. We show that the
phenomenon is generic (e.g. in certain Sobolev spaces) and persists under small
perturbations of initial data, while the resulting blowup is bounded by a
log-modified self-similar asymptotic.
