Math 8803-LEY: Computational Algebraic Geometry
General information

Software and scripts

Math 8803-LEY - Computational Algebraic Geometry - Spring 2014

Place and time:
Skiles 270, 1:35 pm - 2:55 pm, Tue and Thu

Instructor: Anton Leykin
Office: Skiles 250
Office hours: see webpage

The course is an introduction to computational methods of algebraic geometry that are frequently used in applications.

There is no required textbook for this course. It is recommended to have one of the following two books for reference on basic notions:
  • Cox, Little, O'Shea. Using algebraic geometry.
  • Cox, Little, O’Shea. Ideals, Varieties, and Algorithms: an introduction to computational algebraic geometry and commutative algebra.
(both are available for free in electronic form through the GT library)

For additional reading on numerical algebraic geometry use

  • Sommese, Wampler. The numerical solution of systems of polynomials arising in engineering and science.

Below is an imcomplete list of keywords.
  • Basic notions: ideal, variety, ideal-variety correspondence, Hilbert Nullstellensatz, projective space, Newton's method, approximate zero.
  • Symbolic computation: resultant, monomial order, initial ideal, Groebner basis, elimination theory.
  • Numerical algebraic geometry: polynomial homotopy continuation, Bertini's theorem, condition metric, endgame, deflation, regeneration, witness set, numerical irreducible decomposition, monodromy breakup, joins and intersections.

There will be optional homework assignments. In addition, one may choose to study an advanced topic (or a problem) related to the course and make a short presentation at the end of the semester.