Numerical methods : overview. The pseudogap in strong coupling

In this lecture, I will give an overview of the "state of the art" in numerical methods for studying the Hubbard model. This overview will be supplemented by the two seminars on Thursday June 3 (and May 18). I will then show how these methods reveal the existence of a weakly doped pseudogap in the strong coupling regime, which originates in short-range antiferromagnetic correlations. The link with the phenomenology of hole- and electron-doped cuprates will be briefly discussed.