# Fall 2012 MATH 249 001 LEC

Section | Days/Time | Location | Instructor | CCN |
---|---|---|---|---|

001 LEC | MWF 10-11A | 740 EVANS | STURMFELS, B | 54439 |

Units/Credit | Final Exam Group | Enrollment |
---|---|---|

4 | NONE | Limit:30 Enrolled:19 Waitlist:0 Avail Seats:11 [on 11/02/12] |

**Prerequisites:** 250B or equivalent background in commutative algebra. Some exposure to combinatorics, topology and geometry. Students who have taking Math 249 last semester may register for this course as Math 274, CCN 54459.

**Syllabus:** This is a course in Combinatorial Commutative Algebra, based on the text book with Ezra Miller. The book has the following 18 chapters: 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

We shall discuss a different chapter each week, so we shall cover about two-thirds of the book.

**Office:** 925 Evans Hall or up at MSRI

**Required Text:** Ezra Miller and Bernd Sturmfels: Combinatorial Commutative Algebra, Springer Verlag, 2005

**Grading:** Course work consists of a few exercises, class participation, and a term paper. Grades will be based on these.

**Homework:** One exercise per week until October 17.

**Term paper:** Write a paper on a relevant topic of your choice. Collaborations with guests from MSRI are encouraged.

**Course Webpage:** http://math.berkeley.edu/~bernd/math249.html