### Complex Projective Varieties Determined by x^3 + y^3 = z^3 (Fermat's Last Theorem), n = 3. 8.5" X 6.0" X 6.0", Stereolithograph, (c) 1991 Andrew Hanson, Stewart Dickson http://emsh.calarts.edu/~mathart

**Instructor:**Amanda Knecht

Office: Herman Brown 447

Email: knecht@rice.edu

Phone: 2868

**Location:**

Abercrombie A121 (computer lab)

### Time:

Wednesdays, 12:00-12:50

**Description:**

This seminar will focus on the computation of problems in Algebraic Geometry without a heavy emphasis on the theory of the subject. Our goal will be to get a good and thorough understanding of the material through computations in our seminars, outside computer computations, and also final project presentations. Each weekly seminar will consist of a short lecture and then the remaining time will be spent trying to solve a list of weekly computations using Macaulay 2. Outside of each seminar, students are responsible for working some computations out via a computer program and preparing their project for presentation at the end of the semester. Topics will include but are not limited to Gröbner bases, Resultants, Primary Decomposition, Integer Programming, Singular Curves, Gonality of a plane curve, and Invariant Theory of finite groups. Depending on time and interest we will hopefully be able to branch out into more topics in the subject.

**Assessment: **

Attendance/Participation (40%): This course is a seminar, so attendance is crucial.

Project (60%): You will prepare a project and a fifty minute presentation.

Anyone interested in receiving more than one credit hour can arrange to submit a written project along with their presentation.

**Refrences:**:

- David Cox, John Little, and Donal O’Shea:
*Ideals, Varities, and Algorithms*. Springer-Verlag. - David Cox, John Little, and Donal O’Shea:
*Using Algebraic Geometry.*Springer-Verlag. - David Eisenbud, et al.: Computations in Algebraic Geometry with Macaulay 2. Springer.
- Joe Harris:
*Algebraic Geometry*. Springer-Verlag. - Brendan Hassett's Algebraic Geometry Lecture Notes