Sturmfels, Bernd 1962
Overview
Works:  79 works in 296 publications in 4 languages and 5,663 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Author of introduction, Creator, Dedicator 
Classifications:  QA166.6, 511.6 
Publication Timeline
.
Most widely held works by
Bernd Sturmfels
Algorithms in invariant theory
by
Bernd Sturmfels(
)
29 editions published between 1993 and 2008 in 4 languages and held by 909 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
29 editions published between 1993 and 2008 in 4 languages and held by 909 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
Combinatorial commutative algebra
by
Ezra Miller(
)
25 editions published between 2004 and 2007 in English and held by 809 WorldCat member libraries worldwide
"Recent developments are covered; Contains over 100 figures and 250 exercises; Includes complete proofs."Publisher's website
25 editions published between 2004 and 2007 in English and held by 809 WorldCat member libraries worldwide
"Recent developments are covered; Contains over 100 figures and 250 exercises; Includes complete proofs."Publisher's website
Lectures on algebraic statistics
by
Mathias Drton(
)
19 editions published in 2009 in English and held by 527 WorldCat member libraries worldwide
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semialgebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models
19 editions published in 2009 in English and held by 527 WorldCat member libraries worldwide
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semialgebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models
Computational synthetic geometry
by
Jürgen Bokowski(
Book
)
19 editions published between 1987 and 1989 in English and held by 486 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
19 editions published between 1987 and 1989 in English and held by 486 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
Theory of algebraic invariants
by
David Hilbert(
Book
)
7 editions published between 1993 and 2006 in English and held by 432 WorldCat member libraries worldwide
7 editions published between 1993 and 2006 in English and held by 432 WorldCat member libraries worldwide
Gröbner bases and convex polytopes
by
Bernd Sturmfels(
Book
)
9 editions published between 1996 and 1997 in English and held by 351 WorldCat member libraries worldwide
9 editions published between 1996 and 1997 in English and held by 351 WorldCat member libraries worldwide
Solving systems of polynomial equations
by
Bernd Sturmfels(
Book
)
12 editions published in 2002 in English and held by 324 WorldCat member libraries worldwide
12 editions published in 2002 in English and held by 324 WorldCat member libraries worldwide
Applications of computational algebraic geometry : American Mathematical Society short course, January 67, 1997, San Diego, California
(
Book
)
6 editions published in 1998 in English and held by 310 WorldCat member libraries worldwide
6 editions published in 1998 in English and held by 310 WorldCat member libraries worldwide
Gröbner deformations of hypergeometric differential equations
by
Mutsumi Saito(
Book
)
11 editions published between 1999 and 2011 in English and held by 279 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 '
11 editions published between 1999 and 2011 in English and held by 279 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 '
Algebraic statistics for computational biology
(
Book
)
10 editions published in 2005 in English and held by 274 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."BOOK JACKET
10 editions published in 2005 in English and held by 274 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."BOOK JACKET
Combinatorial algebraic geometry : Levico Terme, Italy 2013
by
Italy) Centro internazionale per la ricerca matematica (Trento(
)
5 editions published in 2014 in English and held by 270 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
5 editions published in 2014 in English and held by 270 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
Geometric combinatorics
by
Ezra Miller(
Book
)
9 editions published between 2007 and 2008 in English and held by 194 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
9 editions published between 2007 and 2008 in English and held by 194 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
Applied geometry and discrete mathematics : the Victor Klee festschrift
(
Book
)
8 editions published in 1991 in English and held by 157 WorldCat member libraries worldwide
8 editions published in 1991 in English and held by 157 WorldCat member libraries worldwide
Solving polynomial equations foundations, algorithms, and applications
by
Manuel Bronstein(
)
5 editions published in 2005 in English and held by 45 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." "Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications."Jacket
5 editions published in 2005 in English and held by 45 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." "Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications."Jacket
Oriented Matroids and combinatorial convex geometry
by
Bernd Sturmfels(
Book
)
5 editions published in 1987 in English and held by 22 WorldCat member libraries worldwide
5 editions published in 1987 in English and held by 22 WorldCat member libraries worldwide
Computations in algebraic geometry with Macaulay 2
by
David Eisenbud(
)
2 editions published in 2002 in English and held by 22 WorldCat member libraries 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 22 WorldCat member libraries 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
Minkowski addition of polytopes : computational complexity and applications to Gröbner bases
by
Peter Gritzmann(
Book
)
6 editions published between 1990 and 1992 in English and German and held by 21 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."
6 editions published between 1990 and 1992 in English and German and held by 21 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."
Oriented matroids
by
Anders Björner(
)
4 editions published between 1993 and 1999 in English and held by 21 WorldCat member libraries worldwide
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
4 editions published between 1993 and 1999 in English and held by 21 WorldCat member libraries worldwide
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
Computability of Julia sets
by
Mark Braverman(
)
1 edition published in 2009 in English and held by 16 WorldCat member libraries worldwide
Among all computergenerated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. This book summarizes the knowledge about the computational properties of Julia sets in a selfcontained way. It is suitable for experts and students with interest in theoretical computer science or dynamical systems
1 edition published in 2009 in English and held by 16 WorldCat member libraries worldwide
Among all computergenerated mathematical images, Julia sets of rational maps occupy one of the most prominent positions. This book summarizes the knowledge about the computational properties of Julia sets in a selfcontained way. It is suitable for experts and students with interest in theoretical computer science or dynamical systems
Structural Gröbner basis detection
by
Bernd Sturmfels(
Book
)
3 editions published in 1996 in English and held by 16 WorldCat member libraries worldwide
3 editions published in 1996 in English and held by 16 WorldCat member libraries worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Miller, Ezra 1974 Author Editor
 Sullivant, Seth
 Drton, Mathias Author
 Bokowski, Jürgen Author
 Hilbert, David 18621943 Author
 Cox, David A. Editor
 Manocha, Dinesh N.
 Takayama, Nobuki 1959
 Saito, Mutsumi 1960 Author
 Di Rocco, Sandra Editor
Useful Links
Associated Subjects
Algebra AlgebraData processing Algorithms Artificial intelligence Biometry Combinatorial analysis Combinatorial geometry Commutative algebra Computational complexity Computer science Computer software Convex polytopes Differential equationsAsymptotic theory Distribution (Probability 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 Koszul algebras Linear programming Logic, Symbolic and mathematical Macaulay 2 Mathematical statistics Mathematics Matroids Oriented matroids Polynomials Statistics Toric varieties Vector spaces