FMA150F

Temporary

Algebraic Geometry and Solving Systems of Polynomial Equations

7.5

Third-cycle course

7151 (Centre of Mathematical Sciences / Mathematics)

 -08-24

Professor Thomas Johansson

English
Swedish

If sufficient demand

The aim of the course is to prepare postgraduate students for research using Gröbner bases for solving and interpreting systems of polynomial equations in several variables mainly within algebraic geometry.

Affine varieties and ideals in the ring of polynomials.
Gröbner bases.
Elimination theory.
Algebraic-Geometric Correspondences.
Polynomial and Rational Functions on a Variety.

be able to explain the concept of a Gröbner basis and describe why they are useful for solving systems of polynomial equations.

be able to reproduce key results and give rigorous and detailed proofs of them,

be able to compare key results,

be able to apply the basic techniques, results and concepts of the course to concrete examples and exercises,

be able to combine concepts from the course with other important topics in algebra.

be able to use different methods for solving and for interpreting systems of polynomial equations.

Lectures

Exercises

Project

If the number of participants is small, the course is given as a reading course.

Written exam

Oral exam

Written assignments

Take-home exam.

Failed, pass

FMAN10 Algebraic structures.

Cox, D. & Little, J.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, 2016. ISBN 9783319374277.
Cox, D. & Little, J.: Using Algebraic Geometry. Springer Science & Business Media, 2005. ISBN 9780387207339.

The books are available as e-books via the Mathematics library.

FMA150F

 -08-24

Professor Thomas Johansson