Systems of polynomial equations: from algebraic geometry to industrial applications

Location

BUENOSAIRES
,
Argentina

Dates

to

Presentation

In recent years, an explosive development of algorithms and software constitutes a breakthrough in the field of polynomial system solving, which makes feasible the solution of several problems that had been intractable up to now, and which provides the means necessary for experimentation and conjecture. These algorithms have created a significant interest for effective algebraic geometry and computer algebra among scientists, engineers, and applied mathematicians. The tools of the field, besides algebraic geometry, call upon several aspects of mathematics and theoretical computer science, ranging from numerical methods and differential equations, to discrete geometry, combinatorics and complexity theory. Important applications include computational geometry, computer-aided design, robotics and machine vision. The goal of this school is to provide a general introduction to the field, followed by a survey of recent results and the state-of-the-art, in order to conclude with a discussion of open questions as well as suggestions for new directions of research.

Administrative and scientific coordinators

Alicia Dickenstein (Universidad Buenos Aires,
Argentina
,
alidick@dm.uba.ar
)
Ioannis Emiris (INRIA Sophia-Antipolis,
France
,
Ioannis.Emiris@inria.fr
)

Scientific program

Course 1: "Eigenvalue and eigenvector methods for solving polynomial equations", David Cox (Amherst College, USA)

Course 2: "Introduction to residues and resultants", Alicia Dickenstein (Universidad de Buenos Aires, Argentina)

Course 3: "Computational and applied aspects of solving systems of polynomial equations", Lorenzo Robbiano (Univ. of Genova, Italy)

Course 4: "Toric resultants and applications to geometric modeling", Ioannis Emiris (INRIA Sophia-Antipolis, France)

Course 5: " Ioannis Emiris (INRIA Sophia-Antipolis, France", André Galligo (Univ. de Nice, France)

Course 6: "Symbolic-numeric tools for solving polynomial equations and applications", Bernard Mourrain (INRIA Sophia-Antipolis, France)

Course 7: "Efficient polynomial equation solving: algorithms and complexity", Juan Sabia (Universidad de Buenos Aires, Argentina)

Course 8: "Computational algebraic geometry and the Macaulay2 system", Mike Stillman (Cornell U., USA)

Course 9: "Numerical algebraic geometry", Jan Verschelde (U. Illinois at Chicago, USA)

Website of the school

http://www.cimpa-icpam.org/anciensite/Anglais/AnciensProg/2003/Argentina03.html

How to participate