| Instructor: | Victor Reiner (You can call me "Vic"). |
| Office: Vincent Hall 256, Telephone (with voice mail): 625-6682, E-mail: reiner@math.umn.edu | |
| Classes: | Mon-Wed-Fri 2:30-3:20pm, Vincent Hall 206 (but I will attempt to change the time after the first class to allow attendance at Math 8660 Topics in Probability). |
| Office hours: | Wednesdays at 3:35 PM; one can always arrange to meet me by appointment |
| Course content: |
When studying commutative rings, there are several invariants one wishes to
calculate, some of them homological. In general, these invariants may be hard
to compute. However, for particularly nice classes of rings
(such as quotients of polynomial rings by monomial ideals and semigroup rings),
they can be more tractable, and more fun, due to connections with
combinatorics and combinatorial topology.
This course will be about these kinds of rings, and their connections with combinatorics. Some of the topics we hope to address are:
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| Prerequisites: | Graduate algebra (or some understanding of what polynomial rings, ideals and quotient rings are). Some exposure to simplicial homology and/or homological ideas (e.g. what an exact sequence is) would be helpful, but not absolutely required. |
| Source materials |
There is a text on the subject, in preparation: Combinatorial commutative algebra, by E. Miller and B. Sturmfels. A version is currently (Aug. 19, 2003) at the web-site of Prof. Ezra Miller. I will eventually have Alpha Print distribute a version, once the course enrollment has stabilized.
Here are some other related and potentially useful texts, all on reserve
in the Math Library: |
| Course requirements and grading |
There will be no homeworks or exams. Registered students are
expected to attend regularly, and must either - hand in solutions to 5 homework problems from the text by the last day of class, or - give a talk before the 12th week of the semester on a paper that I approve. Students choosing to give a talk will be expected to meet with me at least once after I have approved the choice of subject, but before they give the talk, to discuss its content. |