Teaching
Current teaching
NMAG468: Dualities in triangulated categories
Lecture notesAssignment 1Assignment 2Assignment 3
These lecture notes will be updated as the course progresses to fix any typos or mistakes. Exercises can be found in the appendix to the lecture notes.
Lectures are Wednesdays 16:30-18:00 in K8 and Thursdays 15:40-17:10 in K9.
For various reasons, there are no classes on the 1st, 2nd, 8th, 15th, 16th of May.
Assignment 3 is due in class on Wednesday 22nd May.
Some recommended exercises:
- Section 5 - Exercises 35, 36
- Section 6 - Exercises 39, 40, 44
- Section 7 - Exercises 45, 46, 47
- Section 8 - Exercises 48, 49, 50.
If you have any questions about the course, or for office hours, please send me an email to arrange a time.
| Date | What we covered | Reference to notes |
|---|---|---|
| 21/02 | Introduction to duality and definition of triangulated categories | Sections 1 and 2.1 |
| 22/02 | The homotopy category of a ring is triangulated | Sections 2.2 and 2.3 |
| 28/02 | Homological functors, the five lemma, and triangulated functors | Sections 2.4 and 2.5 |
| 29/02 | Exercise class | Exercises A.1-A.4 |
| 06/03 | Definition of the derived category of a ring | Section 2.6 up to Lemma 2.30 |
| 07/03 | The derived category is triangulated | Rest of Section 2.6 |
| 13/03 | Calculating maps in the derived category | Section 2.7 |
| 14/03 | Exercise class | Exercises A.5-A.7 |
| 27/03 | Compact objects and Brown representability | Sections 3.1 and 3.2 |
| 03/04 | Homotopy colimits | Section 3.3 |
| 04/04 | Exercise class | Exercises A.16-A.18 |
| 10/04 | The derived category of a commutative ring is tensor-triangulated | Section 4.1 |
| 11/04 | Rigid objects and recap on some algebra | Sections 4.2, 5.1 and 5.2 |
| 17/04 | Local cohomology | Section 5.3 |
| 18/04 | Exercise class | Exercises A.24, A.25, A.33, A.34 |
| 24/04 | Universal property of local cohomology | Section 6.1 |
| 25/04 | Derived completion and localization functors | Sections 6.2 and 7.1 |
| 09/05 | ||
| 22/05 | ||
| 23/05 |
Previous teaching
- Algebra 1 for computer science, Charles University, Winter Semester 2022/2023
- Summer project supervision for third year undergraduate on Morita theory, University of Sheffield, 2019
- Various problem classes, University of Sheffield, 2016-2020