Bridgeland Stability Seminar

Overview

Inspired by the work of Michael Douglas on the Π-Stability of BPS B-Branes in string theory, Tom Bridgeland introduced the notion of stability conditions on triangulated categories, showing that they form a complex manifold with a natural wall and chamber structure. Since then Bridgeland stability has become a well developed theory in the study of derived categories and algebraic geometry underpinning the construction (and often projectivity) of moduli spaces of complexes.

This seminar will be an introduction to Bridgeland stability following the notes of Macrì and Schmidt. The talks will be aimed at graduate students and will assume familiarity with algebraic geometry at the level of Hartshorne or Vakil's Foundations of Algebraic Geometry. Notes and references will be posted here throughout.

Schedule

• Lecture 1 (31 Oct 2025): Coherent Sheaves and Semistable Bundles on Curves - Adam Monteleone, Notes
• Lecture 2 (07 Nov 2025): Stability in Abelian Categories - Tianqi Feng, Notes
• Lecture 3 (18 Nov 2025): Bridgeland Stability Conditions - Fei Peng
• Lecture 4 (21 Nov 2025): Bridgeland Stability and Surfaces - Oliver Li
• Lecture 5 (28 Nov 2025): The Wall and Chamber Stucture Theorem for Surfaces - Marcel Dang, Notes
• Lecture 6 (05 Dec 2025): Bridgeland Stability for Derived Categories of Threefolds - Adam Monteleone

References

• Tom Bridgeland, Stability conditions on triangulated categories, Ann. of Math. 166 (2007), 317–345. journal · arXiv
• Emanuele Macrì and Benjamin Schmidt, Lectures on Bridgeland Stability, arXiv:1607.01262. abs · pdf
• Tom Bridgeland, Stability conditions on K3 surfaces, Duke Math. J. 141 (2008), 241–291. arXiv · journal
• Arend Bayer and Emanuele Macrì, Projectivity and birational geometry of Bridgeland moduli spaces, J. Amer. Math. Soc. 27 (2014), 707–752. journal · arXiv