Stability Conditions

Wednesday seminar, Fall 2008
Seminar location: LUNT 107
Seminar time: Wednesdays, 3-5pm
contact: John Francis, jnkf at northwestern dot com

1. Classical Harder-Narasimhan filtration for coherent sheaves on a curve.
2. Formalize notion of stability, definition of stability function.
3. Examples: quivers and representations.
4. Overview of stability conditions.
5. Physical motivation: Douglas's pi-stability for D-branes, role in mirror symmetry.
6. Braid group actions on categories after Bezrukavnikov and Seidel-Thomas.
7. Donaldson-Thomas theory: Kontsevich-Soibelman and Joyce formulas.
8. T-structures and stability conditions. Structure of spaces of stability conditions.
9. Computations for curves, K3 surfaces, etc.
10. Braid group actions and stability conditions.
11. Donaldson-Thomas invariants and stability conditions.


1. Wed, 1 October 2008, Gabe Kerr: Harder-Narasimhan filtration for coherent sheaves on a curve
2. Wed, 8 October 2008, David Nadler: Stability conditions for vector bundles on low genus curves
3. Wed, 29 October 2008, John Francis: T-structures
4. Wed, 5 November 2008, John Francis: T-structures and slicings
5. Wed, 12 November 2008, Kevin Costello: Whatever he feels like talking about
6. Wed, 19 November 2008, Kevin Costello: Spaces of stability conditions

Stability conditions

1. Bridgeland:,,
2. Huybrechts-Macri-Stellari:
3. Macri:


1. Gaiotto-Moore-Neitzke:
2. Douglas:

Braid actions

1. Bezrukavnikov:
2. Thomas:
3. Khovanov-Seidel:
4. Seidel-Thomas:

Donaldson-Thomas invariants

1. Kontsevich:
2. Joyce:
3. Donaldson-Thomas:
4. Behrend:
5. Kontsevich-Soibelman:


1. Fock-Goncharov:

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