Bernd Sturmfels

Orcid: 0000-0002-6642-1479

  • Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
  • University of California, Berkeley, USA (former)

According to our database1, Bernd Sturmfels authored at least 143 papers between 1986 and 2024.

Collaborative distances:
  • Dijkstra number2 of four.
  • Erdős number3 of two.



In proceedings 
PhD thesis 


Online presence:



Toric geometry of entropic regularization.
J. Symb. Comput., 2024

Bayesian Integrals on Toric Varieties.
SIAM J. Appl. Algebra Geom., March, 2023

Quantum Correlations in the Minimal Scenario.
Quantum, March, 2023

KP solitons from tropical limits.
J. Symb. Comput., 2023

Taylor Polynomials of Rational Functions.
CoRR, 2023

Moment Varieties for Mixtures of Products.
Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, 2023

Voronoi cells of varieties.
J. Symb. Comput., 2022

Publisher Correction: Geometry of Log-Concave Density Estimation.
Discret. Comput. Geom., 2022

Four-Dimensional Lie Algebras Revisited.
CoRR, 2022

Recovery of Plane Curves from Branch Points.
CoRR, 2022

Geometry of Dependency Equilibria.
CoRR, 2022

Marginal Independence Models.
Proceedings of the ISSAC '22: International Symposium on Symbolic and Algebraic Computation, Villeneuve-d'Ascq, France, July 4, 2022

Wasserstein distance to independence models.
J. Symb. Comput., 2021

Primary Ideals and Their Differential Equations.
Found. Comput. Math., 2021

Correction to: The Schläfli Fan.
Discret. Comput. Geom., 2021

Beyond Linear Algebra.
CoRR, 2021

Recovery from Power Sums.
CoRR, 2021

Linear PDE with Constant Coefficients.
CoRR, 2021

The geometry of SDP-exactness in quadratic optimization.
Math. Program., 2020

Brownian motion tree models are toric.
Kybernetika, 2020

The Schläfli Fan.
Discret. Comput. Geom., 2020

Tangent Quadrics in Real 3-Space.
CoRR, 2020

Bad Projections of the PSD Cone.
CoRR, 2020

Learning Paths from Signature Tensors.
SIAM J. Matrix Anal. Appl., 2019

Schottky algorithms: Classical meets tropical.
Math. Comput., 2019

The Geometry of Gaussoids.
Found. Comput. Math., 2019

Sixty-Four Curves of Degree Six.
Exp. Math., 2019

Geometry of Log-Concave Density Estimation.
Discret. Comput. Geom., 2019

Algebraic Analysis of Rotation Data.
CoRR, 2019

D-Modules and Holonomic Functions.
CoRR, 2019

Optimal Transport to a Variety.
Proceedings of the Mathematical Aspects of Computer and Information Sciences, 2019

Distortion Varieties.
Found. Comput. Math., 2018

Real Space Sextics and their Tritangents.
Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation, 2018

Convexity in Tree Spaces.
SIAM J. Discret. Math., 2017

Message from the Editor-in-Chief.
SIAM J. Appl. Algebra Geom., 2017

The Hurwitz form of a projective variety.
J. Symb. Comput., 2017

On the Existence of Epipolar Matrices.
Int. J. Comput. Vis., 2017

Changing Views on Curves and Surfaces.
CoRR, 2017

Congruences and concurrent lines in multi-view geometry.
Adv. Appl. Math., 2017

General Models for Rational Cameras and the Case of Two-Slit Projections.
Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition, 2017

A Clever Elimination Strategy for Efficient Minimal Solvers.
Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition, 2017

Symmetric matrices, Catalan paths, and correlations.
J. Comb. Theory, Ser. A, 2016

Rigid multiview varieties.
Int. J. Algebra Comput., 2016

The Euclidean Distance Degree of an Algebraic Variety.
Found. Comput. Math., 2016

Real Rank Two Geometry.
CoRR, 2016

Nearest Points on Toric Varieties.
CoRR, 2016

Decomposing tensors into frames.
Adv. Appl. Math., 2016

Cayley-Bacharach Formulas.
Am. Math. Mon., 2015

Generic Spectrahedral Shadows.
SIAM J. Optim., 2015

Quartic spectrahedra.
Math. Program., 2015

Duality of Multiple Root Loci.
CoRR, 2015

Computing the Chow Variety of Quadratic Space Curves.
Proceedings of the Mathematical Aspects of Computer and Information Sciences, 2015

Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental.
Proceedings of the Mathematical Aspects of Computer and Information Sciences, 2015

Introduction to Tropical Geometry.
Graduate studies in mathematics 161, American Mathematical Society, ISBN: 978-0-8218-5198-2, 2015

Exact Solutions in Structured Low-Rank Approximation.
SIAM J. Matrix Anal. Appl., 2014

Tropicalization of Classical Moduli Spaces.
Math. Comput. Sci., 2014

Hypersurfaces and Their Singularities in Partial Correlation Testing.
Found. Comput. Math., 2014

Certifying the Existence of Epipolar Matrices.
CoRR, 2014

The euclidean distance degree.
Proceedings of the Symbolic-Numeric Computation 2014, 2014

Maximum likelihood for matrices with rank constraints.
Proceedings of the International Symposium on Symbolic and Algebraic Computation, 2014

Capacity Pre-Log of Noncoherent SIMO Channels Via Hironaka's Theorem.
IEEE Trans. Inf. Theory, 2013

The Universal Kummer Threefold.
Exp. Math., 2013

Algebraic Methods for Structured Low-Rank Approximation.
CoRR, 2013

The Central Curve in Linear Programming.
Found. Comput. Math., 2012

Monomials, Binomials, and Riemann-Roch
CoRR, 2012

Quartic curves and their bitangents.
J. Symb. Comput., 2011

Mixed Discriminants
CoRR, 2011

A Hilbert Scheme in Computer Vision
CoRR, 2011

Commutative Algebra of Statistical Ranking
CoRR, 2011

Combinatorial Types of Tropical Eigenvectors.
CoRR, 2011

Noncoherent SIMO pre-log via resolution of singularities.
Proceedings of the 2011 IEEE International Symposium on Information Theory Proceedings, 2011

The algebraic degree of semidefinite programming.
Math. Program., 2010

Computing Linear Matrix Representations of Helton-Vinnikov Curves
CoRR, 2010

The Convex Hull of a Variety
CoRR, 2010

Computer Algebra in Systems Biology.
Am. Math. Mon., 2009

Matrix Cubes Parameterized by Eigenvalues.
SIAM J. Matrix Anal. Appl., 2009

Convex Rank Tests and Semigraphoids.
SIAM J. Discret. Math., 2009

Toric dynamical systems.
J. Symb. Comput., 2009

Marginal Likelihood Integrals for Mixtures of Independence Models.
J. Mach. Learn. Res., 2009

Computeralgebra in der Systembiologie.
Inform. Spektrum, 2009

Guest Editors' Foreword.
Discret. Comput. Geom., 2009

On the convex hull of a space curve.
CoRR, 2009

How to Draw Tropical Planes.
Electron. J. Comb., 2009

Reconstructing spatiotemporal gene expression data from partial observations.
Bioinform., 2009

Algorithms in Invariant Theory.
Texts & Monographs in Symbolic Computation, Springer, ISBN: 978-3-211-77417-5, 2008

The hyperdeterminant and triangulations of the 4-cube.
Math. Comput., 2008

Three Counter-Examples on Semi-Graphoids.
Comb. Probab. Comput., 2008

Polynomial relations among principal minors of a 4x4-matrix
CoRR, 2008

The Mathematics of Phylogenomics.
SIAM Rev., 2007

Computing tropical varieties.
J. Symb. Comput., 2007

Tropical Implicitization and Mixed Fiber Polytopes
CoRR, 2007

Computing the integer programming gap.
Comb., 2007

Parametric Alignment of <i>Drosophila</i> Genomes.
PLoS Comput. Biol., 2006

Minimizing Polynomials via Sum of Squares over the Gradient Ideal.
Math. Program., 2006

Resultants in genetic linkage analysis.
J. Symb. Comput., 2006

The Newton Polytope of the Implicit Equation
CoRR, 2006

Monomial Dynamical Systems over Finite Fields.
Complex Syst., 2006

Geometry of rank tests.
Proceedings of the Third European Workshop on Probabilistic Graphical Models, 2006

An algebraic geometry approach to nonlinear parametric optimization in control.
Proceedings of the American Control Conference, 2006

Algebraic geometry of Bayesian networks.
J. Symb. Comput., 2005

Toric Ideals of Phylogenetic Invariants.
J. Comput. Biol., 2005

Solving the Likelihood Equations.
Found. Comput. Math., 2005

Short rational functions for toric algebra and applications.
J. Symb. Comput., 2004

Guest Editors' Preface.
Discret. Comput. Geom., 2004

Classification of Six-Point Metrics.
Electron. J. Comb., 2004

Algebraic unimodular counting.
Math. Program., 2003

Higher Lawrence configurations.
J. Comb. Theory, Ser. A, 2003

Elimination Theory in Codimension 2.
J. Symb. Comput., 2002

Guest Editors' Foreword.
Discret. Comput. Geom., 2002

Factorization of Discrete Probability Distributions.
Proceedings of the UAI '02, 2002

Minimizing Polynomial Functions.
Proceedings of the Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, 2001

Generic and Cogeneric Monomial Ideals.
J. Symb. Comput., 2000

Solving algebraic equations in terms of <i>A</i>-hypergeometric series.
Discret. Math., 2000

The search for rational A-hypergeometric functions.
SIGSAM Bull., 1999

Monomial Ideals and Planar Graphs.
Proceedings of the Applied Algebra, 1999

Numerical Schubert Calculus.
J. Symb. Comput., 1998

Variation of cost functions in integer programming.
Math. Program., 1997

Bernstein's Theorem in Affine Space.
Discret. Comput. Geom., 1997

Structural Gröbner Basis Detection
Universität Trier, Mathematik/Informatik, Forschungsbericht, 1996

On Vector Partition Functions.
J. Comb. Theory, Ser. A, 1995

Gröner Bases and Triangulations of the Second Hypersimplex.
Comb., 1995

GRIN: An Implementation of Gröbner Bases for Integer Programming.
Proceedings of the Integer Programming and Combinatorial Optimization, 1995

Grobner Bases - a Computational Approach to Commutative Algebra (Thomas Becker and Volker Weispfenning).
SIAM Rev., 1994

Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Basis.
SIAM J. Discret. Math., 1993

A Note on Polynomial Reduction.
J. Symb. Comput., 1993

Duality and Minors of Secondary Polyhedra.
J. Comb. Theory, Ser. B, 1993

Extension Spaces of Oriented Matroids.
Discret. Comput. Geom., 1993

Algorithms in invariant theory.
Texts and monographs in symbolic computation, Springer, ISBN: 978-3-211-82445-0, 1993

Minkowski Addition of Polytopes: Computational Complexity and Applications to Gröbner Bases
Universität Trier, Mathematik/Informatik, Forschungsbericht, 1992

On the Synthetic Factorization of Projectively Invariant Polynomials.
J. Symb. Comput., 1991

Computational Algebraic Geometry of Projective Configurations.
J. Symb. Comput., 1991

Computing combinatorial decompositions of rings.
Comb., 1991

On the Existence of Certain Smooth Toric Varieties.
Discret. Comput. Geom., 1990

Nonrealizability Proofs in Computational Geometry.
Discret. Comput. Geom., 1990

Unimodular Fans, Linear Codes, and Toric Manifolds.
Proceedings of the Discrete and Computational Geometry: Papers from the DIMACS Special Year, 1990

Arrangements of lines and pseudolines without adjacent triangles.
J. Comb. Theory, Ser. A, 1989

Uniform Oriented Matroids Without the Isotopy Property.
Discret. Comput. Geom., 1989

Proposal for a geometric algebra software package.
SIGSAM Bull., 1989

Coordinate Representation of Order Types Requires Exponential Storage
Proceedings of the 21st Annual ACM Symposium on Theory of Computing, 1989

Some Applications of Affine Gale Diagrams to Polytopes with few Vertices.
SIAM J. Discret. Math., 1988

Neighborly Polytopes and Oriented Matroids.
Eur. J. Comb., 1988

Central and parallel projections of polytopes.
Discret. Math., 1986

On the Coordinatization of Oriented Matroids.
Discret. Comput. Geom., 1986