The Thouless-Anderson-Palmer (TAP) equations are the mean field equations for mixed p-spin glasses on the hypercube. They relate the spin on a site to the field induced on the site by its neighbors. In this talk, we will discuss recent progress regarding the understanding of these equations for a class of mixed p-spin glass models. We will explain a decomposition of the Gibbs measure into conditional laws, each of which satisfies these equations asymptotically. This decomposition satisfies the properties predicted in the physics literature and is essentially unique. If there is time remaining, we will discuss how a family of stochastic processes that arises in the study of this problem relates to the Parisi variational problem and how it can be used to provide PDE based methods for the evaluation of spin statistics. Joint work with Antonio Auffinger (Northwestern University). Speaker(s): Aukosh Jagannath (University of Toronto)