Course Announcement - Fall 2004
Math 249: Combinatorial Commutative Algebra
Instructor: Bernd Sturmfels
Office hours: Tuesdays, 9:45-11:00am
and Fridays, 10:30-11:30am
Contact: bernd at math, 925 Evans, 642 4687
Time and Place: Tuesdays and Thursdays, 8:00-9:30am, 81 Evans Hall
Prerequisites: Math 250B or equivalent background in
commutative algebra, some exposure to combinatorics and geometry.
Students who have already taken a previous version of Math 249
may register for this course as
Math 274, Section 3, CCN 55160.
Course Work
(required for registered students,
encouraged for others):
Seven exercises and a term paper
Exercises:
Please turn in one exercise
every Tuesday, starting on September 7 and ending on October 19.
Choose from the book.
Term paper:
Write a term paper on a topic of your choice related
to Combinatorial Commutative Algebra. Colloborations
welcome.
Important Deadlines for your paper:
Proposal due October 21,
First Draft due November 23,
Final Version due December 9.
The chosen topics for the term papers
and the finished products will be posted on this webpage
(unless you voice objections).
Text: Ezra Miller and Bernd Sturmfels,
Combinatorial Commutative Algebra, Springer, 2004.
To read this book click
here,
or purchase the Reader for Math 249 at Copy Central,
Hearst Ave.
This book will be published by Springer Verlag
(Graduate Texts in Mathematics).
Please e-mail errors and typos to me.
Syllabus:
The book has the following 18 chapters.
A rough plan to discuss a different chapter each week,
so we may cover about two-thirds of the book.
Your input on the selection and order is welcome.
1. Squarefree Monomial Ideals
2. Borel-fixed Monomial Ideals
3. Three-dimensional Staircases
4. Cellular Resolutions
5. Alexander Duality
6. Generic Monomial Ideals
7. Semigroup Algebras
8. Multigraded Polynomial Rings
9. Syzygies of Lattice Ideals
10. Toric Varieties
11. Irreducible and Injective Resolutions
12. Ehrhart Polynomials
13. Local Cohomology
14. Plücker Coordinates
15. Matrix Schubert Varieties
16. Antidiagonal Initial Ideals
17. Minors in Matrix Products
18. Hilbert Schemes of Points