## 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.