Abstract: In this talk I will explore the space of solutions to the conformal crossing equations. By recasting the conformal bootstrap as a non-linear optimization problem, we find an efficient way of converging to the solutions of these equations. Furthermore, by deforming these solutions, I will show that certain solutions corresponding to known theories (e.g Ising) are continuously connected to those of other known theories. Employing these techniques I will explore the space of non-unitary CFTs in 3d and provide evidence for the existence of a 3d "Yang-Lee" model. Time permitting, I will also discuss early results on applications of these methods to deformations of the famous conformal bootstrap islands.