Exact Results in Quantum Theory

Lev Landau's reduction of weakly interacting electrons intoquasiparticles - essentially renormalized but otherwise free particles- forms the basis for a standard model of condensed matter systems.However, a theory to describe transport in strongly interactionsystems has been lacking. Moreover, the notion of "bad metals" hasbeen plausibly linked to "high temperature" superconductivity by PhilAnderson, which has formed a cental tenet for an understanding of thecuprates, for example. Despite multiple decades of effort, there hasbeen no theoretically derived link between the two.Yet, a tremendous amount of advancement in exact and un-biasednumerical methods has been made just in the last 5-10 years. In thistalk I will review some of this work that sheds light into the groundstate and transport properties of simple models for stronglycorrelated electrons. While much remains unresolved, I will give astatus update and discuss a link between transport properties andsuperconductivity.