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.
The scientific program is intended for specialists in the subject, or researchers and students wishing to enter the subject.
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.
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.
 Programa Sul Americano de Apoio às Atividades de Cooperação em Ciência e Tecnologia. |
 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 |
 Fundação José Bonifácio, UFRJ |
 Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro |