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Emerging Applications of Algebraic Geometry

  • Book
  • © 2009

Overview

Editors:
  1. Mihai Putinar

    1. College of Letters & Science, Dept. Mathematics, University of California, Santa Barbara, Santa Barbara, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Seth Sullivant

    1. Cambridge, U.S.A.

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: The IMA Volumes in Mathematics and its Applications (IMA, volume 149)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
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  2. Polynomial Optimization on Odd-Dimensional Spheres

    • John P. D’Angelo, Mihai Putinar
    Pages 1-15

  3. Engineering Systems and Free Semi-Algebraic Geometry

    • Mauricio C. De Oliveira, J. William Helton, Scott A. Mccullough, Mihai Putinar
    Pages 17-61

  4. Algebraic Statistics and Contingency Table Problems: Log-Linear Models, Likelihood Estimation, and Disclosure Limitation

    • Adrian Dobra, Stephen E. Fienberg, Alessandro Rinaldo, Aleksandra Slavkovic, Yi Zhou
    Pages 63-88

  5. Using Invariants for Phylogenetic Tree Construction

    • Nicholas Eriksson
    Pages 89-108

  6. On the Algebraic Geometry of Polynomial Dynamical Systems

    • Abdul S. Jarrah, Reinhard Laubenbacher
    Pages 109-123

  7. A Unified Approach to Computing Real and Complex Zeros of Zero-Dimensional Ideals

    • Jean Bernard Lasserre, Monique Laurent, Philipp Rostalskl
    Pages 125-155

  8. Sums of Squares, Moment Matrices and Optimization Over Polynomials

    • Monique Laurent
    Pages 157-270

  9. Positivity and Sums of Squares: A Guide to Recent Results

    • Claus Scheiderer
    Pages 271-324

  10. Noncommutative Real Algebraic Geometry Some Basic Concepts and First Ideas

    • Konrad Schmüdgen
    Pages 325-350

  11. Open Problems in Algebraic Statistics

    • Bernd Sturmfels
    Pages 351-363

  12. Back Matter

    Pages 365-376
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Keywords

About this book

Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.

Editors and Affiliations

  • College of Letters & Science, Dept. Mathematics, University of California, Santa Barbara, Santa Barbara, USA

    Mihai Putinar

  • Cambridge, U.S.A.

    Seth Sullivant

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