MATH 499/MATH 699: VIGRE Junior Seminar, Computational Algebraic Geometry


Time:

Wednesdays at noon. Feel free to bring your lunch.

Location:

Herman Brown, Room 453

Instructor:

Rena Quandt
Email: quandt@math.rice.edu
Telephone: 713-348-2868 or Rice extension 2868
Office: HB 447

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. 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 is not limited to Grobner bases, Buchberger’s Algorithm, Nullstellensatz, Elimination Theory, and Resultants. Depending on time and interest we will hopefully be able to branch out into more topics in the subject.

Projects:

October 29, Harding Brumby,
Computer Graphics and Projective Space
November 24, Blake Fasching,
Bezier Splines
November 19, Bill Finkenkeller,
Solving Polynomial Equations
Note: Your abstract for your presentation is due exactly one week before you give the presentation.

Textbook:

The material for the seminar will be from several resources, but the book below will probably be the most useful for everyone to have a copy. I do not plan on ordering them through the bookstore, so I would suggest buying it through the internet. Another good source for the seminar will be
Brendan Hassett's Algebraic Geometry Lecture Notes

Grading policy:

The final grade for the one hour seminar will be based on in-class participation (40%) and the final presentation of your project (60%).

Special needs:

Any student with a documented disability needing academic adjustments or accommodations is requested to speak with their instructor during the first two weeks of class. All discussions will remain confidential. Students with disabilities will need to also contact Disability Support Services in the Ley Student Center.