Since 2001 the Scuola Normale Superiore di Pisa has organized the Colloquio De Giorgi a series
of colloquium talks named after Ennio De Giorgi. The Colloquio is addressed to a general
mathematical audience and especially meant to attract graduate students and advanced
undergraduate students. The lectures are intended to be not too technical in fields of wide
interest. They must provide an overview of the general topic possibly in a historical
perspective together with a description of more recent progress. The idea of collecting the
materials from these lectures and publishing them in annual volumes came out recently as a
recognition of their intrinsic mathematical interest and also with the aim of preserving
memory of these events.