Introduction to Bridgeland stability conditions

组织者 / Organizer

邱宇、郑志伟

主讲人 / Speaker

Chunyi Li 李纯毅

University of Warwick

课程安排 / Schedule

15:00-17:00

Jan. 9, 10, 11, 17, 18, 2026

地点 / Venue

C654, Tsinghua University Shuangqing Complex Building A

Introduction to

Bridgeland stability conditions

课程介绍 / Description

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.

主讲人简介 / About the Speaker

Chunyi Li is an associate professor in the Mathematics Institute at the University of Warwick. He obtained his Ph.D. from the University of Illinois at Urbana-Champaign in 2014. Previously, he received his B.S. from Peking University. In 2022, He was awarded the Whitehead Prize for his deep contributions to a wide range of questions in algebraic geometry, in particular in the theory of Bridgeland stability conditions and moduli spaces.

Research Interests

Algebraic geometry, Derived category, Stability condition