Time and place
Seminars take place at Fridays, 10:00–11:30 (Rough plan
- Model categories, simplicial model categories, derived functors
- Derived categories of schemes
- Triangulated categories
- Cotangent complex and deformation theory
- (Stable) infinity categories
- Derived schemes
- Perfect obstruction theories and virtual fundamental classes
- Derived structure on moduli spaces of sheaves
- Derived blow-ups
Literature
Model categories:- [GJ] P. Goerss, J. Jardine, Simplicial homotopy theory, 1999 (Springer Link)
- [GM] Gelfand, Y. Manin, Methods of Homological Algebra, 2nd edition, 2003. (Springer link)
- [J] G. Jasso, Differential graded categories: a representation theoretic approach.
- [K] B. Keller, On differential graded categories, ICM 2006.
- A. Yekutieli, Derived Categories (arXiv:1610.09640)
- [D] A. Dimca, Sheaves in topology. (Springerlink)
- [T] B. Toën, Derived Algebraic Geometry, EMS Surv. Math. Sci. 1 (2014). (Toën's webpage)
- [L] J. Lurie, Derived Algebraic Geometry, Ph D Thesis, MIT 2004. (scanned version, updated? version)
- [SAG] J. Lurie, Spectral Algebraic Geometry, in preparation. (Lurie's webpage)
- [HTT] J. Lurie, Higher Topos Theory, Annals of Mathematics Studies 170, 2009. (Lurie's webpage)
- [HA] J. Lurie, Higher algera, 2017. (Lurie's webpage)
- [G] M. Grot, A short course on infinity-categories, 2015. (arXiv:1007.2925v2)
- [RV] E. Riehl, D. Verity, Infinity category theory from scratch, 2016. (arXiv:1608.05314v1)
Preliminary schedule
| # | Date | Place | Lecturer | Topic | Ref |
|---|---|---|---|---|---|
| 1 | Feb 2 10:30-12:00 | KTH 3418 | David Rydh | Introduction: derived categories, derived schemes, infinity categories | E1 |
| 2 | Feb 9 10:30-12:00 | KTH 3418 | Jeroen Hekking | Model categories: definition, model structure on Top, homotopy category, simplicial sets | [GJ], D2, E2 |
| 3 | Feb 16 10:30-12:00 | KTH 3418 | Jeroen Hekking | Model structures on simplicial sets and chain complexes, derived functors | [GJ], D3, E3 |
| 4 | Feb 23 10:30-12:00 | KTH 3418 | Jeroen Hekking | Simplicial model categories, Yoneda lemma | [GJ], D4 |
| 5 | Mar 2 10:30-12:00 | KTH 3418 | Eric Ahlqvist | Derived categories | [GM], D5 |
| 6 | Mar 9 10:30-12:00 | KTH 3418 | Kristian Moi | Sheaves in topology | [D], D6 |
| - | Mar 16 | — | |||
| 7 | Mar 23 10:30-12:00 | KTH 3418 | Tilman Bauer | Cotangent complex | D7, E7 |
| - | Mar 30 | — | |||
| 8 | Apr 6 10:30-11:30 | KTH 3418 | Tilman Bauer | Cotangent complex II | D8, E8 |
| 9 | Apr 13 10:00-11:30 | KTH 3418 | Jeroen Hekking | Triangulated categories | D9, E9 |
| - | Apr 20 | — | |||
| 10 | Apr 27 10:00-11:30 | KTH 3418 | Wanmin Liu | Bridgeland stability conditions | D10 |
| 11 | May 4 10:00-11:30 | KTH 3418 | David Rydh | Deformation theory | E11 |
| - | May 11 | — | |||
| 12 | May 18 10:00-11:30 | KTH 3418 | Eric Ahlqvist | Artin's axioms | D12 |
| 13 | May 25 10:00-11:30 | KTH 3418 | Eric Ahlqvist | Artin's axioms (cont) | D13 |
| 14 | June 1 10:00-11:30 | KTH 3418 | Kristian Moi | Infinity categories | [HTT], D14 |
| 15 | June 8 10:00-11:30 | KTH 3418 | Dan Petersen | Stable infinity categories | [HA, §1], D15 |