COMS

The geometry of moduli spaces has been widely investigated and it is certainly one of the main subjects in Algebraic Geometry. In particular, moduli spaces of curves gave a major boost to the theory due to their many connections with Theoretical Physics and counting invariants. However, to count invariants it is very useful to apply intersection theory techniques that require the space to be proper, and moduli spaces are usually not proper. The problem of compactifying them is not trivial. Geometric Invariant Theory (GIT) may be a way to tackle the problem, but the limit points can be hard to describe geometrically.

Nowadays, new notions of stability and new techniques related to the minimal model program have been combined with GIT to provide new points of view to attack the problem and, more generally, to study the birational geometry of compactified moduli spaces. This has brought back many important insights again about counting invariants and mirror symmetry and has also been used to study other moduli problems, like the moduli of coherent sheaves or the moduli spaces of higher dimensional varieties.

The lecturers have been chosen among the leading experts of the area. Following the usual policy of the Advanced Schools at CRM, informal notes will be delivered by the speakers to the participants at the beginning of the school.