Sturmfels, Bernd 1962
Overview
Works:  99 works in 385 publications in 4 languages and 6,643 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Author of introduction, Other, Contributor, Dedicator 
Classifications:  QA251.3, 511.6 
Publication Timeline
.
Most widely held works by
Bernd Sturmfels
Combinatorial commutative algebra by
Ezra Miller(
Book
)
22 editions published between 2004 and 2007 in English and held by 462 WorldCat member libraries worldwide
"Recent developments are covered; Contains over 100 figures and 250 exercises; Includes complete proofs."Publisher's website
22 editions published between 2004 and 2007 in English and held by 462 WorldCat member libraries worldwide
"Recent developments are covered; Contains over 100 figures and 250 exercises; Includes complete proofs."Publisher's website
Theory of algebraic invariants by
David Hilbert(
Book
)
8 editions published between 1993 and 2006 in English and held by 430 WorldCat member libraries worldwide
8 editions published between 1993 and 2006 in English and held by 430 WorldCat member libraries worldwide
Algorithms in invariant theory by
Bernd Sturmfels(
Book
)
31 editions published between 1993 and 2008 in 4 languages and held by 413 WorldCat member libraries worldwide
Serves as a textbook for invariant theory and a research monograph that introduces a different approach to the algorithmic side of invariant theory. This title includes several research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems
31 editions published between 1993 and 2008 in 4 languages and held by 413 WorldCat member libraries worldwide
Serves as a textbook for invariant theory and a research monograph that introduces a different approach to the algorithmic side of invariant theory. This title includes several research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems
Computational synthetic geometry by
Jürgen Bokowski(
Book
)
23 editions published between 1987 and 1989 in English and Undetermined and held by 385 WorldCat member libraries worldwide
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research
23 editions published between 1987 and 1989 in English and Undetermined and held by 385 WorldCat member libraries worldwide
Computational synthetic geometry deals with methods for realizing abstract geometric objects in concrete vector spaces. This research monograph considers a large class of problems from convexity and discrete geometry including constructing convex polytopes from simplicial complexes, vector geometries from incidence structures and hyperplane arrangements from oriented matroids. It turns out that algorithms for these constructions exist if and only if arbitrary polynomial equations are decidable with respect to the underlying field. Besides such complexity theorems a variety of symbolic algorithms are discussed, and the methods are applied to obtain new mathematical results on convex polytopes, projective configurations and the combinatorics of Grassmann varieties. Finally algebraic varieties characterizing matroids and oriented matroids are introduced providing a new basis for applying computer algebra methods in this field. The necessary background knowledge is reviewed briefly. The text is accessible to students with graduate level background in mathematics, and will serve professional geometers and computer scientists as an introduction and motivation for further research
Gröbner bases and convex polytopes by
Bernd Sturmfels(
Book
)
13 editions published between 1996 and 1997 in English and held by 376 WorldCat member libraries worldwide
This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry
13 editions published between 1996 and 1997 in English and held by 376 WorldCat member libraries worldwide
This book is about the interplay of computational commutative algebra and the theory of convex polytopes. It centers around a special class of ideals in a polynomial ring: the class of toric ideals. They are characterized as those prime ideals that are generated by monomial differences or as the defining ideals of toric varieties (not necessarily normal). The interdisciplinary nature of the study of Grobner bases is reflected by the specific applications appearing in this book. These applications lie in the domains of integer programming and computational statistics. The mathematical tools presented in the volume are drawn from commutative algebra, combinatorics, and polyhedral geometry
Solving systems of polynomial equations by
Bernd Sturmfels(
Book
)
16 editions published in 2002 in English and held by 339 WorldCat member libraries worldwide
A classic problem in mathematics is solving systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely used across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, and numerous other areas. This book furnishes a bridge across mathematical disciplines and exposes many facets of systems of polynomial equations. It covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical. The set of solutions to a system of polynomial equations is an a
16 editions published in 2002 in English and held by 339 WorldCat member libraries worldwide
A classic problem in mathematics is solving systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely used across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, statistics, and numerous other areas. This book furnishes a bridge across mathematical disciplines and exposes many facets of systems of polynomial equations. It covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical. The set of solutions to a system of polynomial equations is an a
Applications of computational algebraic geometry : American Mathematical Society short course, January 67, 1997, San Diego,
California by
American Mathematical Society(
Book
)
11 editions published in 1998 in English and held by 322 WorldCat member libraries worldwide
11 editions published in 1998 in English and held by 322 WorldCat member libraries worldwide
Algebraic statistics for computational biology(
Book
)
11 editions published in 2005 in English and held by 281 WorldCat member libraries worldwide
"The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These algorithms can be applied to biological problems such as aligning genomes, finding genes, and constructing phylogenies."Jacket
11 editions published in 2005 in English and held by 281 WorldCat member libraries worldwide
"The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These algorithms can be applied to biological problems such as aligning genomes, finding genes, and constructing phylogenies."Jacket
Gröbner deformations of hypergeometric differential equations by
Mutsumi Saito(
Book
)
13 editions published between 1999 and 2011 in English and held by 272 WorldCat member libraries worldwide
In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Gröbner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Gröbner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric partial differentiel equations introduced by Gel'fand, Kapranov and Zelevinsky. The Gröbner deformation of these GKZ hypergeometric systems reduces problems concerning hypergeometric functions to questions about commutative monomial ideals, and thus leads to an unexpected interplay between analysis and combinatorics. This book contains a number of original research results on holonomic systems and hypergeometric functions, and it raises many open problems for future research in this rapidly growing area of computational mathematics '
13 editions published between 1999 and 2011 in English and held by 272 WorldCat member libraries worldwide
In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Gröbner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Gröbner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric partial differentiel equations introduced by Gel'fand, Kapranov and Zelevinsky. The Gröbner deformation of these GKZ hypergeometric systems reduces problems concerning hypergeometric functions to questions about commutative monomial ideals, and thus leads to an unexpected interplay between analysis and combinatorics. This book contains a number of original research results on holonomic systems and hypergeometric functions, and it raises many open problems for future research in this rapidly growing area of computational mathematics '
Geometric combinatorics by
Ezra Miller(
Book
)
10 editions published between 2007 and 2008 in English and held by 207 WorldCat member libraries worldwide
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry
10 editions published between 2007 and 2008 in English and held by 207 WorldCat member libraries worldwide
Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry
Introduction to tropical geometry by
Diane Maclagan(
Book
)
10 editions published in 2015 in English and held by 177 WorldCat member libraries worldwide
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewiselinear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a selfcontained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. Provided by publisher
10 editions published in 2015 in English and held by 177 WorldCat member libraries worldwide
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewiselinear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a selfcontained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. Provided by publisher
Applied geometry and discrete mathematics : the Victor Klee festschrift(
Book
)
12 editions published in 1991 in English and held by 166 WorldCat member libraries worldwide
12 editions published in 1991 in English and held by 166 WorldCat member libraries worldwide
Combinatorial algebraic geometry : Levico Terme, Italy 2013 by
Aldo Conca(
Book
)
12 editions published in 2014 in English and held by 94 WorldCat member libraries worldwide
Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions, and enumerative geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed with a rich combinatorial structure. Relevant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications
12 editions published in 2014 in English and held by 94 WorldCat member libraries worldwide
Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions, and enumerative geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed with a rich combinatorial structure. Relevant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications
Oriented matroids and combinatorial convex geometry by
Bernd Sturmfels(
Book
)
6 editions published between 1986 and 1987 in English and held by 28 WorldCat member libraries worldwide
6 editions published between 1986 and 1987 in English and held by 28 WorldCat member libraries worldwide
Minkowski addition of polytopes : computational complexity and applications to Gröbner bases by
Peter Gritzmann(
Book
)
7 editions published between 1990 and 1992 in English and German and held by 20 WorldCat member libraries worldwide
Using the Minkowski addition of Newton polytopes, we show that the following problem can be solved in polynomial time for any finite set of polynomials [formula], where d is fixed: Does there exist a term order [tau] such that [Tau] is a Gröbner basis for its ideal with respect to [tau]? If not, find an optimal term order for [Tau] with respect to a natural Hilbert function criterion."
7 editions published between 1990 and 1992 in English and German and held by 20 WorldCat member libraries worldwide
Using the Minkowski addition of Newton polytopes, we show that the following problem can be solved in polynomial time for any finite set of polynomials [formula], where d is fixed: Does there exist a term order [tau] such that [Tau] is a Gröbner basis for its ideal with respect to [tau]? If not, find an optimal term order for [Tau] with respect to a natural Hilbert function criterion."
Solving polynomial equations : foundations, algorithms, and applications by
Manuel Bronstein(
)
5 editions published in 2005 in English and held by 14 WorldCat member libraries worldwide
"This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the stateoftheart in several symbolic, numeric, and symbolicnumeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision."Publisher description
5 editions published in 2005 in English and held by 14 WorldCat member libraries worldwide
"This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the stateoftheart in several symbolic, numeric, and symbolicnumeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision."Publisher description
Oriented matroids by
Anders Björner(
Book
)
5 editions published between 1993 and 2000 in English and Undetermined and held by 3 WorldCat member libraries worldwide
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
5 editions published between 1993 and 2000 in English and Undetermined and held by 3 WorldCat member libraries worldwide
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
Computations in algebraic geometry with Macaulay 2 by
David Eisenbud(
Book
)
2 editions published in 2002 in English and held by 1 WorldCat member library worldwide
This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. These expositions will be valuable to both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all. The first part of the book is primarily concerned with introducing Macaulay2, whereas the second part emphasizes the mathematics
2 editions published in 2002 in English and held by 1 WorldCat member library worldwide
This book presents algorithmic tools for algebraic geometry and experimental applications of them. It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out. Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications. The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry. The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems. These expositions will be valuable to both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all. The first part of the book is primarily concerned with introducing Macaulay2, whereas the second part emphasizes the mathematics
Computability of Julia sets by
Mark Braverman(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
"Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computerscreen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge about the computational properties of Julia sets in a selfcontained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems."Jacket
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
"Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computerscreen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge about the computational properties of Julia sets in a selfcontained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems."Jacket
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Related Identities
 Miller, Ezra 1974 Author Editor
 Drton, Mathias Author
 Sullivant, Seth
 Bokowski, Jürgen Author
 Hilbert, David 18621943 Author
 Di Rocco, Sandra 1967 Editor
 Cox, David A. Other Editor
 Manocha, Dinesh N.
 Takayama, Nobuki 1959
 Saito, Mutsumi 1960 Author
Useful Links
Associated Subjects
Algebra AlgebraData processing Algorithms Artificial intelligence Biometry Combinatorial analysis Combinatorial geometry Commutative algebra Commutative rings Computational complexity Computer science Computer software Convex polytopes Differential equationsAsymptotic theory EquationsNumerical solutions Geometry Geometry, Algebraic Geometry, AlgebraicData processing Geometry, Projective GeometryData processing Global analysis (Mathematics) Gröbner bases Hermitian symmetric spaces Hypergeometric functions Information theory Invariants Klee, Victor Koszul algebras Linear programming Logic, Symbolic and mathematical Macaulay 2 Mathematics Matroids Oriented matroids Polynomials Toric varieties Tropical geometry Vector spaces
Alternative Names
Bernd Sturmfels American mathematician
Bernd Sturmfels Duits wiskundige
Bernd Sturmfels matemàtic estatunidenc
Bernd Sturmfels matemático e informático alemão
Bernd Sturmfels matemático estadounidense
Bernd Sturmfels mathématicien allemand
Bernd Sturmfels tysk matematikar
Bernd Sturmfels tysk matematiker
Sturmfels, B. 1962
Sturmfels, B. (Bernd), 1962
Sturmfels, Bernd
Стармфилс, Бернд
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