Topics in Applied Algebraic Geometry

First class Jan. 31 9:15-11 room 3518

Schedule and Notes

General information


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.



Learning outcomes


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,

·       elimination.


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



Course disposition


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

not required.



Examination comment


Take home assignments and possibly oral presentations.



Requirements for final grade


Take home assignments (and oral presentation) completed.

First set of Hmw (Alicia)

Second set of Hmw (Alicia)
Third set of Hmw (Alicia)

First set of Hmw (Sandra)
Second set of Hmw (Sandra)


Course literature:


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.



Contact person.


Sandra Di Rocco




Sandra Di Rocco