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Homotopical Methods
Seminar by Denis-Charles Cisinski and Christian Dahlhausen in winter term 2018/19.
Wednesday 10-12, M 103
Contents
The goal of the seminar is to learn basics of homotopical algebra: a general way to implement methods of algebraic topology to broader context through category theory. These methods are obviously useful in homotopy theory, homotopical algebra, algebraic geometry.Here is a programme for the seminar.
Literature
- W.G. Dwyer, J. Spalinski: Homotopy Theories and Model Categoriesc Handbook of Algebraic Topology, 1995.
- M. Hovey: Model Categories, AMS, 1999.
- M. P.G. Goerss, J.F. Jardine: Simplicial Homotopy Theory, Birkhäuser, 1999.
- D.G. Quillen: Homotopical Algebra, Springer, 1967.
- P. Hirschhorn: Model Categories and their Localizations, AMS, 2003.
Talks
| No. | Date | Title | Speaker |
| 0 | 17.10. | Overview | Denis-Charles Cisinski |
| 1 | 24.10. | Model categories | Christian Dahlhausen |
| 2 | 31.10. | Homotopy Relations | Yassin Mousa |
| 3 | 07.11. | Homotopy categories and localisations | Benedikt Preis |
| 4 | 14.11. | Chain complexes | Flavio Perissinotto |
| 5 | 21.11. | Topological spaces | BM |
| 6 | 28.11. | Derived functors | PH |
| 7 | 05.12. | Homotopy pushouts and homotopy pullbacks | Niklas Kipp |
| 8 | 12.12. | The small object argument | NP |
| 9 | 19.12. | Cofibrantly generated model categories | Paul Baernreuther |
| 10 | 09.01. | Simplicial sets | Harry Gindi |
| 11 | 16.01. | Principal fibrations on a simplicial group | Sebastian Wolf |
| 12 | 23.01. | seminar cancelled | |
| 13 | 30.01. | Reedy model structures | Denis-Charles Cisinski |
| 14 | 06.02. | Model categories and higher categories | Denis-Charles Cisinski |
Organisatorial remarks
In order to obtain credits for the course, you shall:- Give a talk of 80 minutes (so that the remaining 10 minutes are free for questions and discussions).
- Be regularly present at the seminar and participate actively (do not hesitate to ask questions if you do not understand something).
- Prepare a one-sheet handout including the main aspects of your talk as well as some small exercises for the other participants (so that they are encouraged to think about the content of the talk again). We offer to print the handouts for you if you hand them in sufficiently early.
- Submit a written elaboration or a copy of handwritten notes of your talk
- latest on the day of your talk via
- sending an email to both of the organisers with an electronic file and
- bringing one paper copy to the talk.
- Show up at the latest on Monday in the week of your talk at one of the organisers' office hours with a draft of your elaboration or your notes. This serves to show the organisers that you are well-prepared. The earlier you come, the more time you have to clarify questions about your talk.
- Your work will be graded and credited as written in the Prüfungsordnung.