Precision many-body theory for the Hubbard model and beyond: the knowns, the known unknowns, and the unknown unknownns*

This talk will summarize the present status of our knowledge of the equilibrium properties of the two dimensional Hubbard model, including the regimes of magnetism, superconductivity and the pseudogap and the correlation functions relevant for dynamics. Results obtained by different methods will be compared and regimes of relative agreement and of relative uncertainty will be delineated. The relation of the results to data on cold atom systems and copper-oxide high transition temperature superconductors will be discussed and open issues will be highlighted. Brief mention of nonequilibrium physics will be made.