In a recent preprint with Luis Silvestre we show that smooth solutions to the homogeneous Landau equation do not break down in finite time for a broad range of potentials -- including Coulomb. This result, which relies on showing the monotonicity for the Fisher information, is made possible by three ingredients: 1) a "lifting" of the Landau equation to a linear degenerate parabolic PDE in double the number of variables, 2) a decomposition of this linear PDE in terms of rotations and 3) a functional inequality on the sphere that is closely related to the log-Sobolev inequality. In this talk I will describe these ingredients starting by motivating some of them for the simpler case of the heat equation.