In recent work with Luis Silvestre we rule out blow ups for the space homogeneous Landau equation, the fundamental equation in plasma physics. This follows from the monotonicity of an important functional in statistics — the Fisher information. This was made possible by a new lifting procedure which (somewhat surprisingly!) relates kinetic equations to linear parabolic equations. These linear equations are in fact quite simple -- they are given by parametric families of solutions to the heat equation on the two-dimensional sphere. The convexity of the Fisher information functional as well as the symmetries of the equation play an important role in the proof. Time allowing I will put this result in context in light of recent results, specially result of Imbert, Silvestre, and Villani ruling out blow up for the space homogeneous Boltzmann equation and recent work of Bedrossian, Chen, Gualdani Ji, Vicol, and Yang where they construct implosion singularities in the space inhomogeneous setting (all the more notable as this is done for potentials covered by the space homogeneous non-blow up result, indicating the important role of transport in singularity formation).