2nd Latin American School and Workshop on Polynomial Systems

Angra dos Reis, RJ, Brasil - Feb 28 to March 4, 2005

NEW: Pictures of the conference

Description and scope

The theoretical study of the solution set of polynomial equations gave rise to classical areas in mathematics, such as Algebra or Algebraic Geometry. Polynomial systems arising from practical or industrial applications require a much finer study of the system structure than what is available from classical tools.

This conference is interdisciplinary due to the nature of its object. The analysis of equation structure involves concepts of Convex Geometry, Symplectic Geometry, Complexity, Numerical Analysis, etc... In addition, efficient algorithms to solve systems of polynomial equations combine tools and concepts of Computational Algebra, Computational Algebraic Geometry, Differential Geometry, Linear Programming, Sparse Numerical Linear Algebra, Combinatorics, etc...

Applications of polynomial systems arise in many areas, such as mechanical engineering, chemistry and bio-chemistry, control theory, computer graohics, mathematical physics... Special attention here will be given to applications to statistics.

Target audience

The school is intended for a public ranging from first year graduate students in mathematics to research scientists. There will be a short course and five survey lectures during the morning.

The scientific program is intended for specialists in the subject, or researchers and students wishing to enter the subject.

Five lectures by Bernd Sturmfels

Algebraic Geometry of Statistical Models

The five lectures offer an introduction to algebraic methods in statistics. Many statistical models for discrete data, in particular those used in machine learning and computational biology, can be regarded as algebraic varieties inside a high-dimensional probability simplex. While some of these models correspond to classical geometric objects (e.g. Segre varieties and their secant varieties), others pose new and unexpected challenges for algebraic geometers. Conversely, computational algebraic geometry has a lot to offer for statistical analysis since certain key problems, such as computing maximum likelihood estimates and checking identifiability, lead to systems of polynomial equations.

Bernd Sturmfels' five lectures will be based on his forthcoming book with Lior Pachter, titled "Algebraic Statistics for Computational Biology".

The lectures will correspond to sections in the book as follows:

Lecture 1: Statistical Models (Sections 1.1 and 1.2)

Lecture 2: Maximum Likelihood (Sections 3.3 and 1.3)

Lecture 3: Markov Models (Sections 1.4 and 1.5)

Lecture 4: Phylogenetics (Sections 2.4 and 3.5)

Lecture 5: Alignment and Inference (Sections 2.2 and 3.4)

A draft of the book is available electronically here. Course participants are strongly encouraged to take a look at the above sections before traveling to Angra dos Reis.

Survey lectures

Alicia Dickenstein Toric Ideals and Applications

Gregorio Malajovich Mixed volume and sparse homotopy

Laurent Busé Elimination Theory, Commutative Algebra and Applications

Ioannis Emiris Sparse Elimination and Geometric Applications

Jean-Pierre Dedieu Newton iteration and applications.

Invited and contributed lectures.

There will also be invited and contributed talks. The extended deadline for submissions is November 15, 2004.

List of Participants

Complete program


Financial support for participants

Requests for financial support are now closed.

Deadlines for registration

You may still register for the school, but the deadlines for talks and support have expired.

Registration Form

Local information.

The meeting will be held at the Portogalo Suíte Hotel, Estrada Rio Santos km 461, Angra dos Reis, RJ, Brasil. (Distance to Rio de Janeiro: 130 km. Distance to Angra dos Reis: 15km). Reservations should be made through the conference agent. Hotel bookings include breakfast, lunch, dinner, and two coffee breaks. Conference rates per night (tax included) are: R$ 220,50 SGL/ R$ 304,50 DBL/ R$ 441,00 TPL.
Hotel Reservation form for Brazilian participants.
Hotel Reservation form for non-Brazilian participants not supported by the conference.

At this time, the exchange rate oscillates around R$ 2,54 = US$ 1,00 (as of feb 19th) plus or minus 10%.

Previous conference.

The first Latin American Workshop and School on Polynomial Systems was held in Buenos Aires, from 14 to 26 of july 2003, with around 70 registered participants.

Organizing Committee

Alicia Dickenstein(*), Departamento de Matemática, FCEyN, Universidad de Buenos Aires.
Alvaro Rittatore, Centro de Matemática, Universidad de la República.
Gregorio Malajovich(*), Departamento de Matemática Aplicada, Universidade Federal do Rio de Janeiro.
Ioannis Emiris, Department of Informatics & Telecommunications, National University of Athens.
Vilmar Trevisan, Instituto de Matemática, Universidade Federal do Rio Grande do Sul.
(*) Chairs


Other conferences on the subject.

Please check Foundations of Computational Mathematics and also ISSAC and MEGA.

Conference organized by:

Departamento de Matemática Aplicada - UFRJ Instituto do Milênio: Avanço Global e Integrado da Matemática Brasileira.


Programa Sul Americano de Apoio às Atividades de Cooperação em Ciência e Tecnologia.
International Mathematical Union
International Mathematical Union

Subproyecto 03 del PAV 03 de Matemática, SECyT, Argentina.

Conselho Nacional de Desenvolvimento Científico e Tecnológico - Edital de Eventos
The Abdus Salam International Center for Theoretical Physics
The Abdus Salam International Center for Theoretical Physics

Fundação José Bonifácio, UFRJ

Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro


This page is mantained by Gregorio Malajovich.