Homological Algebra
This study group takes place on Wednesdays at 3pm in S3.05.
Talks:
- 2nd October: Chain Complexes (Ruari Walker).
- 9th October: Long Exact Sequences (Ruari Walker); Chain Homotopies (Robin Cussol).
- 16th October: Mapping Cones (Robin Cussol); (Co)homological Functors (Peter Latham).
- 23rd October: Projective and Injective Resolutions (Peter Latham).
- 28th October: Derived Functors I. (Keith Brown).
- 6th November: Derived Functors II. (Keith Brown).
- 13th November: Limits and Colimits I. (Shaun Stevens).
- 20th November: Limits and Colimits II. Balancing Ext and Tor. (Shaun Stevens).
- 27th November: Tor and Flatness. (Peng Xu).
- 2nd December: Ext and Extensions. (Vanessa Miemietz).
- 11th December: Derived Functor of lim. (Lewis Topley).
- 18th December: Kuenneth Formula and Universal Coefficient Theorem. (Bob Gray).
- 15th January: The Homotopy Category. (Ruari Walker).
- 22th January: Triangulated Categories. (Robin Cussol).
- 29th January: Localisation I. (Peter Latham).
- 5th February: Localisation II, Serre subcategories I. (Peter Latham/Vanessa Miemietz).
- 12th February: Serre subcategories II, The derived category (triangulation). (Vanessa Miemietz/Keith Brown).
- 19th February: The derived category (existence and properties). (Keith Brown).
- 26th February: no talk: schoolboard meeting.
- 5th March: The derived category as a homotopy category of projectives/injectives. (Lewis Topley).
- 19th March: Total derived functors I. (Robin Cussol).
- 26th March: Total derived functors II. (Ruari Walker).
References
- Weibel, Charles A. An introduction to homological algebra. Cambridge Studies in Advanced Mathematics, 38. Cambridge University Press, Cambridge, 1994.
- Hilton, P. J.; Stammbach, U. A course in homological algebra. Second edition. Graduate Texts in Mathematics, 4. Springer-Verlag, New York, 1997.
- Rotman, Joseph J. An introduction to homological algebra. Second edition. Universitext. Springer, New York, 2009.