Emerging Applications of Algebraic Geometry

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Mihai Putinar, Seth Sullivant
Springer Science & Business Media, 2008 M12 10 - 376 páginas

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.

 

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POLYNOMIAL OPTIMIZATION ON ODDDIMENSIONAL SPHERES
1
ENGINEERING SYSTEMS AND FREE SEMIALGEBRAIC GEOMETRY
17
ALGEBRAIC STATISTICS AND CONTINGENCY TABLE PROBLEMS LOGLINEAR MODELS LIKELIHOOD ESTIMATION AND DISCLOSUR...
63
USING INVARIANTS FOR PHYLOGENETIC TREE CONSTRUCTION
89
ON THE ALGEBRAIC GEOMETRY OF POLYNOMIAL DYNAMICAL SYSTEMS
109
SUMS OF SQUARES MOMENT MATRICES AND OPTIMIZATION OVER POLYNOMIALS
157
POSITIVITY AND SUMS OF SQUARESA GUIDE TO RECENT RESULTS
271
NONCOMMUTATIVE REAL ALGEBRAIC GEOMETRY SOMEBASIC CONCEPTS AND FIRST IDEAS
325
OPEN PROBLEMS IN ALGEBRAIC STATISTICS
351
LIST OF WORKSHOP PARTICIPANTS
365
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