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).
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, 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:
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