Well, this web page didn’t get as much attention as I thought it might this semester. I’ll keep it here as an historical document.
My thanks to all the students in the course for a very enlightening semester!
Memo to the future: Since there was no syllabus (also no homework, exams, or quizzes) for this course, you might wonder what exactly was going on here. MAT 830 was a one-credit graduate course in Combinatorial Commutative Algebra. The goal of the course was to learn enough tools of CCA to be able to work through the proof of one or two of the more important applications to Combinatorics. In particular, I tried to motivate the course by discussing the Upper Bound Conjecture and the Anand-Dumir-Gupta Conjectures.
We used (the first chapter of) the recent book of Miller and Sturmfels. Thanks are due to Jeremy Martin for posting online notes from an informal seminar in Stanley-Reisner theory; they helped me chart a course through the material. In the end, we were able to sketch the proof of the Upper Bound Conjecture. (Not bad, considering we started from the definition of a graded ring!)
Most course meetings were devoted to lectures from the students. Dan Zacharia and I gave bookending lectures.