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 reactionnetworks
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 massaction
kinetics

The 7bar 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).
Eligibility
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.
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, OShea, 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), 6583. Prefinal
version available at:
http://mate.dm.uba.ar/~alidick/papers/MCA0215.pdf

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
Examiner
Sandra
Di Rocco