Dimension Theory of Noetherian Rings, Winter 2018

Samir Canning,

The goal of this seminar is to understand the dimension theory of Noetherian rings. Participants will give lectures on various topics, roughly laid out below. We want to understand the algebra behind statements like "the dimension of affine n-space over a ring R is n+dim(R)." In particular, we don't restrict ourselves to the case of finite type algebras over fields, but will obtain results about this case along the way. The chosen topic should be of interest to algebraic geometers, algebraists, and number theorists alike. Moreover, the theoretical part of the lectures should be understandable by anyone who has taken a first course in commutative algebra: say 200C. On the other hand, we appreciate examples from diverse areas of mathematics, and it is not expected that every person in the room understands every example. If you need help preparing your talk or finding resources, ask Samir Canning.


  1. The organizers of this seminar are Samir Canning and Thomas Grubb.
  2. All updates will be made on this website.
  3. The talks are 50 minutes long.
  4. Time and place: Room B402A, Monday 10:00 -- 10:50 AM.
  5. First meeting: January 8. Everybody interested please attend.
The following list of lectures is tentative (especially the topics of the lectures). If you want to give a talk, email Samir Canning or Thomas Grubb.

List of lectures:

  1. Jan 8. Samir Canning. Introduction and Hilbert Polynomials. Notes
  2. Jan 15. No seminar for MLK Day.
  3. Jan 24. Thomas Grubb. Characterization of Dimension in terms of Hilbert Polynomials (DATE CHANGE, ROOM CHANGE B412)
  4. Feb 5. Shubham Sinha. Height and Systems of Parameters
  5. Feb 12. Samir Canning. Depth
  6. Feb 19. No seminar for Presidents' Day
  7. Feb 26. No seminar
  8. Mar 5. No seminar for Arizona Winter School
  9. Mar 12. Iacopo Brivio. Cohen Macaulay Rings and Modules
  10. Mar 19. Woonam Lim. (Universally) Catenary Rings and the Dimension Formula