Abstract: In 2006, Krieger, Schlag and Tataru constructed a family of blow up solutions to the 2+1 dimensional wave map equation with unit sphere as its target. The singularity formation of these solutions is due to the concentration of energy. Another key feature of this family is that it exhibits a continuum of blow up rates. However, due to its delicate construction, the stability of this family was not clear. In this talk, I will present our work in which we show that these solutions are actually stable under equivariant perturbations. This is a joint work with Joachim Krieger.