Computational Homological Algebra (Projects)

Jean-Louis Koszul
Triangulated Category
Alexander Beilinson
Task
Learn a new theorem in homological algebra and communicate it in written form.
Requirements
  • Each student will focus on a different result.
  • The written document will introduce/motivate, correctly state, and prove a theorem. It will also include at least one interesting example, construction, or special case illustrating the theorem. The article will be as self-contained as possible. The new document must be typed, about eight pages in length (with one inch margins and a 12pt font), and be available in PDF format. By design, this assignment is very open-ended.
Assessment
Project grades will be computed as follows:
Due Date Element Weight
2022.11.14 outline 10%
2022.11.28 rough draft 20%
2022.12.05 feedback 20%
2022.12.15 project 50%
Advice
Paul R. Halmos and Steven L. Kleiman each provide some suggestions on how to present mathematics.
Potential Topics
The following results are natural candidates:
  1. 2-categories— JASON PALOMBARO
  2. Amitsur complex
  3. bar complex— TAO GONG
  4. Čech complex— CEYHUN ELMACIOGLU
  5. de Rham complex— DANIEL MARTCHENKOV
  6. Eagon-Northcott type complexes
  7. Galois cohomology— CURTIS WILSON
  8. flat resolutions— CALVIN FLETCHER
  9. Kan extension— CHIRANTAN MUKHERJEE
  10. Koszul algebras— OUSSAMA HAMZA
  11. Koszul homology and regular sequences— VISHAL BHATOY
  12. Local cohomology— BENJAMIN JEFFERS
  13. Matlis duality
  14. matrix factorizations— DEEPANSHU PRASAD
  15. minimal resolutions
  16. semi-injective resolutions— JAROD PALUBISKI
  17. Tate complexes— SAMIK MITRA