Math 732: Bridgeland stability

Winter 2021, University of Michigan

Instructor: Alex Perry (arper@umich.edu)

Time and place: Tuesdays and Thursdays 1-2:30 pm on Zoom

Syllabus

References

Foundational papers

• Stability conditions on triangulated categories, Bridgeland.
• Stability conditions on K3 surfaces, Bridgeland.

Surveys

• Lectures on Bridgeland stability, Macrì and Schmidt.
• A tour to stability conditions on derived categories, Bayer.
• Conditions de stabilité et géométrie birationnelle, Charles.

Derived categories (ordered from less to more detailed)

• Derived categories for the working mathematician, Thomas.
• Fourier-Mukai transforms in algebraic geometry, Huybrechts.
• Methods of homological algebra, Gelfand and Manin.
• Derived categories and Derived categories of schemes chapters of the Stacks Project.

Quivers

• Note on finiteness of global dimension for acyclic quivers, Farnsteiner.