Enrico Arbarello (Sapienza Università di Roma) : "Bridgeland theory and its applications in algebraic geometry"

COURSE DESCRIPTION:
The aim of the course is to give an introduction to Bridgeland theory together with various application of this theory to classical algebraic geometry: Brill-Noether Theory, curves on K3 surfaces, etc.
We give give a bird-eye view on these subjects, providing proofs only here and there but giving many examples.

PREREQUISITES: Basic algebraic geometry, including schemes and sheaves (covered by Hartshorne and Schafarevich textbooks) and basic homological algebra, including derived categories and cohomologies of sheaves (covered by Gelfand-Manin).

COURSE PROGRAM:
Quot schemes and moduli (6 lectures)
Classical algebraic geometry (5 or 6 lectures):
    - Brill-Noether theory
    - K3 surfaces
Bridgeland theory and applications (5 or 4 lectures)