Exceptional collections on rational surfaces and related mod
题目：Exceptional collections on rational surfaces and related moduli problems
After recalling the definition of (strong) exceptional collection of line bundles on a smooth projective surface X, I will introduce several open problems and conjectures in this area and give solutions or counter-examples. Then I will talk about the realization of rational surfaces as moduli spaces of stable representations of Belinson quiver. If time permits, I will talk about some applications of exceptional collections to classical problem in algebraic geometry, say moduli space of semistable sheaves on rational surfaces.