Geometric methods in representation theory. Vol. 2

This second volume gathers part of the texts issued from the summer school « Geometric methods in representation theory » (Grenoble, 16 June - 4 July, 2008). They comprise expanded versions of lecture notes for the course of Schiffmann, as well as ten research or survey articles. These texts give an overview of the representation theory of quivers, chiefly from a geometric perspective. The methods and results cover a wide range of mathematical domains : algebra and representation theory (Hall algebras, canonical and crystal bases, cluster categories, modular representations...), algebraic geometry (flag varieties, moduli spaces, symplectic singularities...), homological methods (perverse sheaves, exceptional collections...) In view of the diverseness of the topics, the reader is invited to consult the introductions of the texts for detailed overviews of their respective contents.