Announcements
Syllabus
Software and scripts

Place and time:

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

Instructor: Anton Leykin

Office: Skiles 250

Email: leykin@math.gatech.edu

Webpage: http://people.math.gatech.edu/~aleykin3/math8803spr14

Office hours: see webpage

Description:

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

Textbook:

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.

Topics:

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.

Homework/Projects/Presentations:

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.