Explore the construction of weak solutions for the Landau equation through a comprehensive lecture that delves into approximations of solutions to the Boltzmann equation in a grazing collision limit. Presented by I. Gamba from The University of Texas at Austin, this 69-minute talk is part of the Advanced School & Workshop on Nonlocal Partial Differential Equations and Applications to Geometry, Physics and Probability. Gain insights into complex mathematical concepts and their applications in physics and probability theory as you delve into this advanced topic in the field of partial differential equations.