组织者：邱宇，郑志伟

Abstract: The notion of stability conditions on a triangulated category was introduced by Bridgeland in the early 2000s, inspired by Douglas’s concept of $\Pi$-stability. Although its original motivation comes from mathematical physics, the theory has found a wide range of applications over the past two decades. In this mini-course, I will discuss several of its key applications in algebraic geometry, focusing in particular on positivity theory, birational geometry, and moduli spaces.

The first three lectures are intended for a general audience in algebraic geometry. I will cover topics including classical stability for vector bundles, the Bogomolov inequality, Hilbert schemes, the Beilinson quiver, triangulated categories, and stability conditions on curves and surfaces. The final two lectures are aimed at participants with a more specialized interest in the subject. Topics will include wall-crossing phenomena on the stability manifold, stability conditions on higher-dimensional varieties, and families of stability conditions.