This course will introduce the necessary background in computational and numerical Algebraic Geometry and guide the students through two important applications: dynamics of biochemical reaction-networks
and approximation of motions in robotics.
The students will get a deep understanding of the mathematical theory and the algorithms used in practice in numerical algebraic geometry. After completing the course, the student should be able to work with:
· Gröbner bases,
· binomial ideals,
· homotopy continuation,
· basic intersection theory,
Course main content
The course will focus on two main applications of computational algebraic geometrical tools:
- Biochemical reaction networks modeled by mass-action kinetics
- The 7-bar inverse problem in Kinematics
The introductory material will include:
- Algebraic Varieties
- Basics on intersections of Algebraic subvarieties
- Directed graphs
- binomial ideals
- elimination and implicitization
The course is given as a series of lectures (approx 15 x 2h).
Knowledge of basic algebra. A basic knowledge of algebraic geometry is desirable but
Take home assignments and possibly oral presentations.
Requirements for final grade
Take home assignments
(and oral presentation) completed.
Notes from the lectures. Literature reference will include:
- Cox, Little, O-Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra .
- Biochemical reaction networks: an invitation for algebraic geometers.
MCA 2013, Contemporary Mathematics 656 (2016), 65-83. Pre-final
version available at:
- Selig, Geometric Fundamentals of Robotics,
- Sommese, Wampler, The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. World Scientific press.
Sandra Di Rocco
Sandra Di Rocco