Stability Conditions

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

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.

Schedule

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

References
Stability conditions

1. Bridgeland: http://arxiv.org/abs/math/0611510, http://arxiv.org/abs/math/0212237,
http://arxiv.org/abs/math/0207021
2. Huybrechts-Macri-Stellari: http://arxiv.org/abs/math/0608430
3. Macri: http://arxiv.org/abs/0705.3794

Physics

1. Gaiotto-Moore-Neitzke: http://arxiv.org/abs/0807.4723
2. Douglas: http://arxiv.org/abs/math/0207021

Braid actions

1. Bezrukavnikov: http://arxiv.org/abs/math/0604445
2. Thomas: http://arxiv.org/abs/math/0212214
3. Khovanov-Seidel: http://arxiv.org/abs/math/0006056
4. Seidel-Thomas: http://arxiv.org/abs/math/0001043

Donaldson-Thomas invariants

1. Kontsevich: www.mpim-bonn.mpg.de/preprints/send?bid=3352
2. Joyce: http://arxiv.org/abs/hep-th/0607039
3. Donaldson-Thomas:
4. Behrend: http://arxiv.org/abs/math/0507523
5. Kontsevich-Soibelman:

Clusters

1. Fock-Goncharov: http://arxiv.org/abs/math/0702397

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