Edit Profile (opens in new tab) Sturmfels, Bernd Compute Distance To: Compute Author ID: sturmfels.bernd Published as: Sturmfels, Bernd; Sturmfels, B. Homepage: http://math.berkeley.edu/~bernd/ External Links: MGP · ORCID · Wikidata · Math-Net.Ru · dblp · GND · IdRef · theses.fr Documents Indexed: 295 Publications since 1986, including 15 Books 11 Contributions as Editor · 1 Further Contribution Biographic References: 3 Publications Co-Authors: 239 Co-Authors with 263 Joint Publications 4,425 Co-Co-Authors all top 5 Co-Authors 40 single-authored 12 Pachter, Lior 9 Ranestad, Kristian 8 Dickenstein, Alicia M. 8 Thomas, Rekha R. 8 Uhler, Caroline 6 Bokowski, Jürgen G. 6 De Loera, Jesús A. 6 Hoşten, Serkan 6 Sullivant, Seth 5 Billera, Louis J. 5 Cattani, Eduardo H. 5 Eisenbud, David 5 Joswig, Michael 5 Miller, Ezra 5 Morton, Jason 5 Peeva, Irena V. 5 Shiu, Anne 5 Sottile, Frank 5 Takayama, Nobuki 5 Vinzant, Cynthia 5 Yu, Josephine 5 Zwiernik, Piotr 4 Améndola, Carlos 4 Çelik, Türkü Özlüm 4 Drton, Mathias 4 Lin, Shaowei 4 Nie, Jiawang 4 Ottaviani, Giorgio Maria 4 Ren, Qingchun 4 Richter-Gebert, Jürgen 4 Robeva, Elina 4 Saito, Mutsumi 4 Santos, Francisco 4 Seigal, Anna Leah 4 Zelevinskiĭ, Andreĭ V. 4 Ziegler, Günter Matthias 3 Barlow, Miriam 3 Bayer, David Allen 3 Beerenwinkel, Niko 3 Cartwright, Dustin A. 3 Diaconis, Persi Warren 3 Draisma, Jan 3 Eriksson, Nicholas 3 Gritzmann, Peter 3 Huber, Birkett 3 Huggins, Peter 3 Kapranov, Mikhail M. 3 Kleinschmidt, Peter 3 Kohn, Kathlén 3 Laubenbacher, Reinhard C. 3 Michałek, Mateusz 3 Mira, Portia M. 3 Onn, Shmuel 3 Panizzut, Marta 3 Parrilo, Pablo A. 3 Plaumann, Daniel 3 Speyer, David E. 3 Stillman, Michael Eugene 2 Agostini, Daniele 2 Avramov, Luchezar L. 2 Björner, Anders 2 Breiding, Paul 2 Brodsky, Sarah B. 2 Cifuentes, Diego 2 Crona, Kristina 2 Cueto, María Angélica 2 Develin, Mike 2 Di Rocco, Sandra 2 Feichtner, Eva Maria 2 Fevola, C. 2 Fulton, William 2 Green, Mark Lee 2 Greene, Devin C. V. 2 Hauenstein, Jonathan D. 2 Hemmecke, Raymond 2 Horobeţ, Emil 2 Huh, June 2 Huneke, Craig L. 2 Jamneshan, Asgar 2 Jensen, Anders Nedergaard 2 Kahle, Thomas 2 Kaihnsa, Nidhi 2 Khetan, Amit 2 Kileel, Joe 2 Kubjas, Kaie 2 Kummer, Mario Denis 2 Las Vergnas, Michel 2 Maclagan, Diane 2 Meza, Juan C. 2 Montúfar, Guido F. 2 Namin, Mahsa Sayyary 2 Ottem, John Christian 2 Pedersen, Paul S. 2 Reiner, Victor 2 Rostalski, Philipp 2 Roudneff, Jean-Pierre 2 Sam, Steven V. 2 Sanyal, Raman 2 Smith, Karen E. 2 Tevelev, Jenia ...and 141 more Co-Authors all top 5 Serials 15 Journal of Symbolic Computation 9 Journal of Algebra 9 Discrete & Computational Geometry 7 Advances in Mathematics 7 Foundations of Computational Mathematics 6 Linear Algebra and its Applications 6 Mathematical Programming. Series A. Series B 5 Le Matematiche 5 Mathematische Zeitschrift 5 Notices of the American Mathematical Society 4 Bulletin of Mathematical Biology 4 Journal of Combinatorial Theory. Series A 4 Journal of Pure and Applied Algebra 4 SIAM Journal on Discrete Mathematics 4 Advances in Geometry 4 Journal of Algebraic Statistics 3 American Mathematical Monthly 3 Mathematics of Computation 3 The Annals of Statistics 3 Compositio Mathematica 3 Duke Mathematical Journal 3 Mathematische Annalen 3 Proceedings of the American Mathematical Society 3 Advances in Applied Mathematics 3 Combinatorica 3 Journal of the American Mathematical Society 3 SIAM Journal on Matrix Analysis and Applications 3 Journal of Algebraic Combinatorics 3 Documenta Mathematica 3 Algebraic Statistics 2 Discrete Mathematics 2 Beiträge zur Algebra und Geometrie 2 American Journal of Mathematics 2 Canadian Journal of Mathematics 2 Geometriae Dedicata 2 Journal für die Reine und Angewandte Mathematik 2 Mathematica Scandinavica 2 Mathematika 2 Topology 2 IMRN. International Mathematics Research Notices 2 Proceedings of the National Academy of Sciences of the United States of America 2 Experimental Mathematics 2 Journal of Algebraic Geometry 2 The Electronic Journal of Combinatorics 2 Mathematical Research Letters 2 Bernoulli 2 Encyclopedia of Mathematics and Its Applications 2 Graduate Studies in Mathematics 2 Graduate Texts in Mathematics 2 Lecture Notes in Mathematics 2 Mathematical Sciences Research Institute Publications 2 Algorithms and Computation in Mathematics 2 PLOS ONE 2 Texts & Monographs in Symbolic Computation 1 IEEE Transactions on Information Theory 1 Israel Journal of Mathematics 1 Nonlinearity 1 Scandinavian Journal of Statistics 1 Mathematics Magazine 1 Acta Mathematica Vietnamica 1 Annales de l’Institut Fourier 1 Annals of the Institute of Statistical Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Bulletin of the London Mathematical Society 1 Collectanea Mathematica 1 Journal of Combinatorial Theory. Series B 1 Journal of the London Mathematical Society. Second Series 1 Kybernetika 1 Memoirs of the Faculty of Science. Series A. Mathematics 1 Michigan Mathematical Journal 1 Proceedings of the Japan Academy. Series A 1 Proceedings of the London Mathematical Society. Third Series 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Results in Mathematics 1 Revista de la Unión Matemática Argentina 1 SIAM Journal on Numerical Analysis 1 SIGSAM Bulletin 1 Tohoku Mathematical Journal. Second Series 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Probability Theory and Related Fields 1 Complex Systems 1 The Annals of Applied Probability 1 International Journal of Algebra and Computation 1 Aequationes Mathematicae 1 SIAM Review 1 Bulletin of the American Mathematical Society. New Series 1 Applicable Algebra in Engineering, Communication and Computing 1 SIAM Journal on Optimization 1 Combinatorics, Probability and Computing 1 International Journal of Computer Vision 1 Journal of Mathematical Sciences. University of Tokyo 1 Selecta Mathematica. New Series 1 Statistica Sinica 1 Mathematical Finance 1 Vietnam Journal of Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Annals of Combinatorics ...and 25 more Serials all top 5 Fields 162 Algebraic geometry (14-XX) 120 Commutative algebra (13-XX) 77 Convex and discrete geometry (52-XX) 65 Combinatorics (05-XX) 60 Computer science (68-XX) 42 Statistics (62-XX) 32 Operations research, mathematical programming (90-XX) 28 Linear and multilinear algebra; matrix theory (15-XX) 26 Numerical analysis (65-XX) 22 Biology and other natural sciences (92-XX) 17 Geometry (51-XX) 11 Field theory and polynomials (12-XX) 10 General and overarching topics; collections (00-XX) 9 Special functions (33-XX) 9 Probability theory and stochastic processes (60-XX) 7 Associative rings and algebras (16-XX) 7 Group theory and generalizations (20-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Algebraic topology (55-XX) 4 History and biography (01-XX) 4 Nonassociative rings and algebras (17-XX) 3 Number theory (11-XX) 3 Functions of a complex variable (30-XX) 3 Information and communication theory, circuits (94-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Partial differential equations (35-XX) 2 Differential geometry (53-XX) 2 Systems theory; control (93-XX) 2 Mathematics education (97-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Ordinary differential equations (34-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Manifolds and cell complexes (57-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 271 Publications have been cited 7,304 times in 4,442 Documents Cited by ▼ Year ▼ Gröbner bases and convex polytopes. Zbl 0856.13020Sturmfels, Bernd 419 1996 Combinatorial commutative algebra. Zbl 1090.13001Miller, Ezra; Sturmfels, Bernd 349 2005 Introduction to tropical geometry. Zbl 1321.14048Maclagan, Diane; Sturmfels, Bernd 268 2015 Solving systems of polynomial equations. Zbl 1101.13040Sturmfels, Bernd 204 2002 Algebraic algorithms for sampling from conditional distributions. Zbl 0952.62088Diaconis, Persi; Sturmfels, Bernd 182 1998 Binomial ideals. Zbl 0873.13021Eisenbud, David; Sturmfels, Bernd 166 1996 The tropical Grassmannian. Zbl 1065.14071Speyer, David; Sturmfels, Bernd 162 2004 Oriented matroids. 2nd ed. Zbl 0944.52006Björner, Anders; Las Vergnas, Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter 145 1999 Algorithms in invariant theory. Zbl 0802.13002Sturmfels, Bernd 143 1993 First steps in tropical geometry. Zbl 1093.14080Richter-Gebert, Jürgen; Sturmfels, Bernd; Theobald, Thorsten 140 2005 Algebraic statistics for computational biology. Zbl 1108.62118 125 2005 Oriented matroids. Zbl 0773.52001Björner, Anders; Las Vergnas, Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter M. 118 1993 Tropical convexity. Zbl 1054.52004Develin, Mike; Sturmfels, Bernd 118 2004 Gröbner deformations of hypergeometric differential equations. Zbl 0946.13021Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki 112 2000 Lectures on algebraic statistics. Zbl 1166.13001Drton, Mathias; Sturmfels, Bernd; Sullivant, Seth 95 2009 A polyhedral method for solving sparse polynomial systems. Zbl 0849.65030Huber, Birkett; Sturmfels, Bernd 85 1995 Minimizing polynomial functions. Zbl 1099.13516Parrilo, Pablo A.; Sturmfels, Bernd 83 2003 Toric dynamical systems. Zbl 1188.37082Craciun, Gheorghe; Dickenstein, Alicia; Shiu, Anne; Sturmfels, Bernd 82 2009 Matroid polytopes, nested sets and Bergman fans. Zbl 1092.52006Feichtner, Eva Maria; Sturmfels, Bernd 80 2005 The number of eigenvalues of a tensor. Zbl 1277.15007Cartwright, Dustin; Sturmfels, Bernd 79 2013 Cellular resolutions of monomial modules. Zbl 0909.13011Bayer, Dave; Sturmfels, Bernd 77 1998 Monomial resolutions. Zbl 0909.13010Bayer, Dave; Peeva, Irena; Sturmfels, Bernd 73 1998 Fiber polytopes. Zbl 0762.52003Billera, Louis J.; Sturmfels, Bernd 72 1992 Combinatorial commutative algebra. Zbl 1066.13001Miller, Ezra; Sturmfels, Bernd 70 2005 On the Newton polytope of the resultant. Zbl 0798.05074Sturmfels, Bernd 69 1994 Intersection theory on toric varieties. Zbl 0885.14025Fulton, William; Sturmfels, Bernd 68 1997 Computing tropical varieties. Zbl 1121.14051Bogart, T.; Jensen, A. N.; Speyer, D.; Sturmfels, B.; Thomas, R. R. 67 2007 On the rank of a tropical matrix. Zbl 1095.15001Develin, Mike; Santos, Francisco; Sturmfels, Bernd 67 2005 Minimizing polynomials via sum of squares over the gradient ideal. Zbl 1134.90032Nie, Jiawang; Demmel, James; Sturmfels, Bernd 64 2006 Algorithms in invariant theory. 2nd ed. Zbl 1154.13003Sturmfels, Bernd 64 2008 The Euclidean distance degree of an algebraic variety. Zbl 1370.51020Draisma, Jan; Horobeţ, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha R. 62 2016 On the toric algebra of graphical models. Zbl 1104.60007Geiger, Dan; Meek, Christopher; Sturmfels, Bernd 61 2006 Constructions and complexity of secondary polytopes. Zbl 0714.52004Billera, Louis J.; Filliman, Paul; Sturmfels, Bernd 58 1990 Computational synthetic geometry. Zbl 0683.05015Bokowski, Jürgen; Sturmfels, Bernd 54 1989 Tropical discriminants. Zbl 1166.14033Dickenstein, Alicia; Feichtner, Eva Maria; Sturmfels, Bernd 53 2007 Toric ideals of phylogenetic invariants. Zbl 1391.13058Sturmfels, Bernd; Sullivant, Seth 52 2005 Algebraic geometry of Bayesian networks. Zbl 1126.68102Garcia, Luis David; Stillman, Michael; Sturmfels, Bernd 51 2005 Tropical mathematics. Zbl 1227.14051Speyer, David; Sturmfels, Bernd 49 2009 Chow polytopes and general resultants. Zbl 0780.14027Kapranov, M. M.; Sturmfels, Bernd; Zelevinsky, Andrei V. 47 1992 Multigraded Hilbert schemes. Zbl 1072.14007Haiman, Mark; Sturmfels, Bernd 46 2004 Minkowski addition of polytopes: Computational complexity and applications to Gröbner bases. Zbl 0798.68157Gritzmann, Peter; Sturmfels, Bernd 45 1993 Syzygies of codimension 2 lattice ideals. Zbl 0918.13006Peeva, Irena; Sturmfels, Bernd 43 1998 Intersection theory on spherical varieties. Zbl 0819.14019Fulton, William; MacPherson, Robert; Sottile, F.; Sturmfels, Bernd 42 1995 The algebraic degree of semidefinite programming. Zbl 1184.90119Nie, Jiawang; Ranestad, Kristian; Sturmfels, Bernd 41 2010 Gröbner bases of toric varieties. Zbl 0714.14034Sturmfels, Bernd 40 1991 Product formulas for resultants and Chow forms. Zbl 0792.13006Pedersen, Paul; Sturmfels, Bernd 40 1993 Sagbi bases of Cox-Nagata rings. Zbl 1202.14053Sturmfels, Bernd; Xu, Zhiqiang 38 2010 Gröbner bases and Stanley decompositions of determinantal ideals. Zbl 0685.13005Sturmfels, Bernd 37 1990 Toric hyperkähler varieties. Zbl 1029.53054Hausel, Tamás; Sturmfels, Bernd 36 2002 Elimination theory for tropical varieties. Zbl 1157.14038Sturmfels, Bernd; Tevelev, Jenia 36 2008 Generic lattice ideals. Zbl 0905.13005Peeva, Irena; Sturmfels, Bernd 33 1998 Maximal minors and their leading terms. Zbl 0776.13009Sturmfels, Bernd; Zelevinsky, Andrei V. 33 1993 Bounds on degrees of projective schemes. Zbl 0828.14040Sturmfels, Bernd; Ngô Viêt Trung; Vogel, Wolfgang 32 1995 Sparse elimination theory. Zbl 0837.13011Sturmfels, Bernd 32 1993 On vector partition functions. Zbl 0837.11055Sturmfels, Bernd 32 1995 How to draw tropical planes. Zbl 1195.14080Herrmann, Sven; Jensen, Anders; Joswig, Michael; Sturmfels, Bernd 32 2009 The maximum likelihood degree. Zbl 1123.13019Catanese, Fabrizio; Hoşten, Serkan; Khetan, Amit; Sturmfels, Bernd 32 2006 Quartic curves and their bitangents. Zbl 1214.14049Plaumann, Daniel; Sturmfels, Bernd; Vinzant, Cynthia 32 2011 Quotients of toric varieties. Zbl 0762.14023Kapranov, M. M.; Sturmfels, Bernd; Zelevinsky, Andrei V. 30 1991 Syzygies of oriented matroids. Zbl 1022.13002Novik, Isabella; Postnikov, Alexander; Sturmfels, Bernd 29 2002 Combinatorial secant varieties. Zbl 1107.14045Sturmfels, Bernd; Sullivant, Seth 29 2006 Equations defining toric varieties. Zbl 0914.14022Sturmfels, Bernd 28 1997 Variation of cost functions in integer programming. Zbl 0888.90125Sturmfels, Bernd; Thomas, Rekha R. 28 1997 Computing linear matrix representations of Helton-Vinnikov curves. Zbl 1328.14093Plaumann, Daniel; Sturmfels, Bernd; Vinzant, Cynthia 28 2012 Orbitopes. Zbl 1315.52001Sanyal, Raman; Sottile, Frank; Sturmfels, Bernd 28 2011 Computing combinatorial decompositions of rings. Zbl 0739.68051Sturmfels, Bernd; White, Neil 27 1991 Algorithms for the Quillen-Suslin theorem. Zbl 0747.13020Logar, Alessandro; Sturmfels, Bernd 27 1992 Generic and cogeneric monomial ideals. Zbl 0955.13008Miller, Ezra; Sturmfels, Bernd; Yanagawa, Kohji 27 2000 Higher Lawrence configurations. Zbl 1036.52018Santos, Francisco; Sturmfels, Bernd 27 2003 Affine buildings and tropical convexity. Zbl 1133.52003Joswig, Michael; Sturmfels, Bernd; Yu, Josephine 27 2007 Polynomial equations and convex polytopes. Zbl 0988.52021Sturmfels, Bernd 26 1998 Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Zbl 1440.62255Sturmfels, Bernd; Uhler, Caroline 26 2010 Cellular strings on polytopes. Zbl 0812.52007Billera, Louis J.; Kapranov, M. M.; Sturmfels, Bernd 25 1994 Computing Hopf bifurcations. I. Zbl 0948.37037Guckenheimer, John; Myers, Mark; Sturmfels, Bernd 24 1997 Lattice walks and primary decomposition. Zbl 0962.05010Diaconis, Persi; Eisenbud, David; Sturmfels, Bernd 24 1998 Four counterexamples in combinatorial algebraic geometry. Zbl 1018.14022Sturmfels, Bernd 24 2000 Tropical geometry of statistical models. Zbl 1135.62302Pachter, Lior; Sturmfels, Bernd 23 2004 Extension spaces of oriented matroids. Zbl 0783.52009Sturmfels, Bernd; Ziegler, Günter M. 23 1993 Initial complexes of prime ideals. Zbl 0877.13025Kalkbrener, Michael; Sturmfels, Bernd 23 1995 Algebraic factor analysis: tetrads, pentads and beyond. Zbl 1111.13020Drton, Mathias; Sturmfels, Bernd; Sullivant, Seth 23 2007 Toric geometry of cuts and splits. Zbl 1180.13040Sturmfels, Bernd; Sullivant, Seth 23 2008 Hyperdeterminantal relations among symmetric principal minors. Zbl 1130.15005Holtz, Olga; Sturmfels, Bernd 23 2007 The hyperdeterminant and triangulations of the 4-cube. Zbl 1194.52016Huggins, Peter; Sturmfels, Bernd; Yu, Josephine; Yuster, Debbie S. 22 2008 Phylogenetic algebraic geometry. Zbl 1106.14050Eriksson, Nicholas; Ranestad, Kristian; Sturmfels, Bernd; Sullivant, Seth 22 2005 Exact solutions in structured low-rank approximation. Zbl 1318.14057Ottaviani, Giorgio; Spaenlehauer, Pierre-Jean; Sturmfels, Bernd 22 2014 How to shell a monoid. Zbl 0893.20048Peeva, Irena; Reiner, Victor; Sturmfels, Bernd 21 1998 Residues and resultants. Zbl 0933.14033Cattani, Eduardo; Dickenstein, Alicia; Sturmfels, Bernd 21 1998 Computing multidimensional residues. Zbl 0882.13020Cattani, E.; Dickenstein, A.; Sturmfels, Bernd 21 1996 Algebraic boundaries of Hilbert’s SOS cones. Zbl 1273.13043Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd 21 2012 Bernstein’s theorem in affine space. Zbl 0891.65055Huber, B.; Sturmfels, Bernd 20 1997 Gröbner bases of lattices, corner polyhedra, and integer programming. Zbl 0863.90115Sturmfels, Bernd; Weismantel, Robert; Ziegler, Günter M. 20 1995 Likelihood geometry. Zbl 1328.14004Huh, June; Sturmfels, Bernd 20 2014 A Hilbert scheme in computer vision. Zbl 1284.13035Aholt, Chris; Sturmfels, Bernd; Thomas, Rekha 20 2013 Simplicial cells in arrangements and mutations of oriented matroids. Zbl 0654.05019Roudneff, Jean-Pierre; Sturmfels, Bernd 20 1988 Cutting corners. Zbl 0955.52008Onn, Shmuel; Sturmfels, Bernd 18 1999 Convex rank tests and semigraphoids. Zbl 1198.62038Morton, Jason; Pachter, Lior; Shiu, Anne; Sturmfels, Bernd; Wienand, Oliver 18 2009 Siphons in chemical reaction networks. Zbl 1198.92020Shiu, Anne; Sturmfels, Bernd 18 2010 Solving the likelihood equations. Zbl 1097.13035Hosten, Serkan; Khetan, Amit; Sturmfels, Bernd 18 2005 On the coordinatization of oriented matroids. Zbl 0615.05022Bokowski, Jürgen; Sturmfels, Bernd 18 1986 Polytopal and nonpolytopal spheres. An algorithmic approach. Zbl 0639.52004Bokowski, Jürgen; Sturmfels, Bernd 18 1987 Invitation to nonlinear algebra. Zbl 1477.14001Michałek, Mateusz; Sturmfels, Bernd 6 2021 Primary ideals and their differential equations. Zbl 07434418Cid-Ruiz, Yairon; Homs, Roser; Sturmfels, Bernd 4 2021 Discrete statistical models with rational maximum likelihood estimator. Zbl 1465.62184Duarte, Eliana; Marigliano, Orlando; Sturmfels, Bernd 2 2021 Bad projections of the PSD cone. Zbl 1467.14120Jiang, Yuhan; Sturmfels, Bernd 2 2021 Maximum likelihood estimation for totally positive log-concave densities. Zbl 1473.62048Robeva, Elina; Sturmfels, Bernd; Tran, Ngoc; Uhler, Caroline 1 2021 Estimating linear covariance models with numerical nonlinear algebra. Zbl 1461.62230Sturmfels, Bernd; Timme, Sascha; Zwiernik, Piotr 7 2020 The Schläfli Fan. Zbl 07242482Joswig, Michael; Panizzut, Marta; Sturmfels, Bernd 4 2020 The geometry of SDP-exactness in quadratic optimization. Zbl 1445.90075Cifuentes, Diego; Harris, Corey; Sturmfels, Bernd 3 2020 Twenty-seven questions about the cubic surface. Zbl 1454.14104Ranestad, Kristian; Sturmfels, Bernd 2 2020 An octanomial model for cubic surfaces. Zbl 1451.14116Panizzut, Marta; Sertöz, Emre; Sturmfels, Bernd 2 2020 3264 conics in a second. Zbl 1437.14053Breiding, Paul; Sturmfels, Bernd; Timme, Sascha 2 2020 Brownian motion tree models are toric. Zbl 07332783Sturmfels, Bernd; Uhler, Caroline; Zwiernik, Piotr 1 2020 Varieties of signature tensors. Zbl 1411.14068Améndola, Carlos; Friz, Peter; Sturmfels, Bernd 7 2019 The geometry of gaussoids. Zbl 1453.13076Boege, Tobias; D’Alì, Alessio; Kahle, Thomas; Sturmfels, Bernd 5 2019 Learning paths from signature tensors. Zbl 1469.14116Pfeffer, Max; Seigal, Anna; Sturmfels, Bernd 4 2019 Schottky algorithms: classical meets tropical. Zbl 07066492Chua, Lynn; Kummer, Mario; Sturmfels, Bernd 4 2019 Geometry of log-concave density estimation. Zbl 1416.62202Robeva, Elina; Sturmfels, Bernd; Uhler, Caroline 2 2019 Sixty-four curves of degree six. Zbl 1440.14270Kaihnsa, Nidhi; Kummer, Mario; Plaumann, Daniel; Namin, Mahsa Sayyary; Sturmfels, Bernd 2 2019 Algebraic identifiability of Gaussian mixtures. Zbl 1423.14284Améndola, Carlos; Ranestad, Kristian; Sturmfels, Bernd 10 2018 Learning algebraic varieties from samples. Zbl 1481.13040Breiding, Paul; Kališnik, Sara; Sturmfels, Bernd; Weinstein, Madeleine 8 2018 Nearest points on toric varieties. Zbl 1393.14049Helmer, Martin; Sturmfels, Bernd 6 2018 Distortion varieties. Zbl 1408.14191Kileel, Joe; Kukelova, Zuzana; Pajdla, Tomas; Sturmfels, Bernd 3 2018 Changing views on curves and surfaces. Zbl 1388.14160Kohn, Kathlén; Sturmfels, Bernd; Trager, Matthew 2 2018 The Hurwitz form of a projective variety. Zbl 1359.14043Sturmfels, Bernd 16 2017 Real rank geometry of ternary forms. Zbl 1390.14179Michałek, Mateusz; Moon, Hyunsuk; Sturmfels, Bernd; Ventura, Emanuele 15 2017 Eigenconfigurations of tensors. Zbl 1360.15011Abo, Hirotachi; Seigal, Anna; Sturmfels, Bernd 9 2017 Convexity in tree spaces. Zbl 1370.05040Lin, Bo; Sturmfels, Bernd; Tang, Xiaoxian; Yoshida, Ruriko 8 2017 Real rank two geometry. Zbl 1401.14229Seigal, Anna; Sturmfels, Bernd 5 2017 Congruences and concurrent lines in multi-view geometry. Zbl 1367.14022Ponce, Jean; Sturmfels, Bernd; Trager, Mathew 4 2017 How to flatten a soccer ball. Zbl 1406.14042Kubjas, Kaie; Parrilo, Pablo A.; Sturmfels, Bernd 2 2017 Combinatorial algebraic geometry. Selected papers from the 2016 apprenticeship program, Ottawa, Canada, July–December 2016. Zbl 1387.14014 1 2017 The Euclidean distance degree of an algebraic variety. Zbl 1370.51020Draisma, Jan; Horobeţ, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha R. 62 2016 Algebraic systems biology: a case study for the Wnt pathway. Zbl 1356.92038Gross, Elizabeth; Harrington, Heather A.; Rosen, Zvi; Sturmfels, Bernd 18 2016 Exponential varieties. Zbl 1345.14048Michałek, Mateusz; Sturmfels, Bernd; Uhler, Caroline; Zwiernik, Piotr 15 2016 Duality of multiple root loci. Zbl 1346.14126Lee, Hwangrae; Sturmfels, Bernd 9 2016 Moment varieties of Gaussian mixtures. Zbl 1361.13017Améndola, Carlos; Faugère, Jean-Charles; Sturmfels, Bernd 9 2016 Tropicalization of del Pezzo surfaces. Zbl 1375.14218Ren, Qingchun; Shaw, Kristin; Sturmfels, Bernd 8 2016 Tensors and their eigenvectors. Zbl 1352.15030Sturmfels, Bernd 8 2016 Decomposing tensors into frames. Zbl 1331.15019Oeding, Luke; Robeva, Elina; Sturmfels, Bernd 5 2016 Symmetric matrices, Catalan paths, and correlations. Zbl 1344.05042Sturmfels, Bernd; Tsukerman, Emmanuel; Williams, Lauren 3 2016 Computing the Chow variety of quadratic space curves. Zbl 1460.14132Bürgisser, Peter; Kohn, Kathlén; Lairez, Pierre; Sturmfels, Bernd 2 2016 Maximum likelihood estimates for Gaussian mixtures are transcendental. Zbl 1460.62081Améndola, Carlos; Drton, Mathias; Sturmfels, Bernd 1 2016 Introduction to tropical geometry. Zbl 1321.14048Maclagan, Diane; Sturmfels, Bernd 268 2015 Fixed points of the EM algorithm and nonnegative rank boundaries. Zbl 1308.62035Kubjas, Kaie; Robeva, Elina; Sturmfels, Bernd 13 2015 A family of quasisymmetry models. Zbl 1344.05155Kateri, Maria; Mohammadi, Fatemeh; Sturmfels, Bernd 12 2015 Moduli of tropical plane curves. Zbl 1349.14043Brodsky, Sarah; Joswig, Michael; Morrison, Ralph; Sturmfels, Bernd 12 2015 Quartic spectrahedra. Zbl 1328.14091Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd; Vinzant, Cynthia 12 2015 Tensors of nonnegative rank two. Zbl 1312.15033Allman, Elizabeth S.; Rhodes, John A.; Sturmfels, Bernd; Zwiernik, Piotr 10 2015 Generic spectrahedral shadows. Zbl 1346.14132Sinn, Rainer; Sturmfels, Bernd 9 2015 Cayley-Bacharach formulas. Zbl 1346.14083Ren, Qingchun; Richter-Gebert, Jürgen; Sturmfels, Bernd 4 2015 Rational design of antibiotic treatment plans: a treatment strategy for managing evolution and reversing resistance. Zbl 1375.92032Mira, Portia M.; Crona, Kristina; Greene, Devin; Meza, Juan C.; Sturmfels, Bernd; Barlow, Miriam 2 2015 Correction: “Rational design of antibiotic treatment plans: a treatment strategy for managing evolution and reversing resistance”. Zbl 1376.92025Mira, Portia M.; Crona, Kristina; Greene, Devin; Meza, Juan C.; Sturmfels, Bernd; Barlow, Miriam 2 2015 Exact solutions in structured low-rank approximation. Zbl 1318.14057Ottaviani, Giorgio; Spaenlehauer, Pierre-Jean; Sturmfels, Bernd 22 2014 Likelihood geometry. Zbl 1328.14004Huh, June; Sturmfels, Bernd 20 2014 Maximum likelihood for matrices with rank constraints. Zbl 1345.62043Hauenstein, Jonathan; Rodriguez, Jose Israel; Sturmfels, Bernd 13 2014 Tropicalization of classical moduli spaces. Zbl 1305.14031Ren, Qingchun; Sam, Steven V.; Sturmfels, Bernd 9 2014 Hypersurfaces and their singularities in partial correlation testing. Zbl 1308.62110Lin, Shaowei; Uhler, Caroline; Sturmfels, Bernd; Bühlmann, Peter 4 2014 The Euclidean distance degree. Zbl 1346.68281Draisma, Jan; Horobeţ, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha 2 2014 The number of eigenvalues of a tensor. Zbl 1277.15007Cartwright, Dustin; Sturmfels, Bernd 79 2013 A Hilbert scheme in computer vision. Zbl 1284.13035Aholt, Chris; Sturmfels, Bernd; Thomas, Rekha 20 2013 The entropic discriminant. Zbl 1284.15006Sanyal, Raman; Sturmfels, Bernd; Vinzant, Cynthia 15 2013 Mixed discriminants. Zbl 1273.13051Cattani, Eduardo; Cueto, María Angélica; Dickenstein, Alicia; Di Rocco, Sandra; Sturmfels, Bernd 13 2013 Binary cumulant varieties. Zbl 1274.13048Sturmfels, Bernd; Zwiernik, Piotr 12 2013 The universal Kummer threefold. Zbl 1312.14103Ren, Qingchun; Sam, Steven V.; Schrader, Gus; Sturmfels, Bernd 11 2013 Monomials, binomials and Riemann-Roch. Zbl 1272.13017Manjunath, Madhusudan; Sturmfels, Bernd 10 2013 Elliptic curves in honeycomb form. Zbl 1312.14142Chan, Melody; Sturmfels, Bernd 9 2013 Dualities. Zbl 1360.90195Rostalski, Philipp; Sturmfels, Bernd 7 2013 Combinatorial types of tropical eigenvectors. Zbl 1269.15009Sturmfels, Bernd; Tran, Ngoc Mai 6 2013 Matrices with eigenvectors in a given subspace. Zbl 1272.15010Ottaviani, Giorgio; Sturmfels, Bernd 5 2013 Toric cubes. Zbl 1315.52011Engström, Alexander; Hersh, Patricia; Sturmfels, Bernd 4 2013 Capacity pre-log of noncoherent SIMO channels via Hironaka’s theorem. Zbl 1364.94430Morgenshtern, Veniamin I.; Riegler, Erwin; Yang, Wei; Durisi, Giuseppe; Lin, Shaowei; Sturmfels, Bernd; Bölcskei, Helmut 1 2013 Computing linear matrix representations of Helton-Vinnikov curves. Zbl 1328.14093Plaumann, Daniel; Sturmfels, Bernd; Vinzant, Cynthia 28 2012 Algebraic boundaries of Hilbert’s SOS cones. Zbl 1273.13043Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd 21 2012 The central curve in linear programming. Zbl 1254.90108De Loera, Jesús A.; Sturmfels, Bernd; Vinzant, Cynthia 15 2012 Commutative algebra of statistical ranking. Zbl 1316.13042Sturmfels, Bernd; Welker, Volkmar 11 2012 On the convex hull of a space curve. Zbl 1245.14033Ranestad, Kristian; Sturmfels, Bernd 10 2012 Graphical models for correlated defaults. Zbl 1270.91092Filiz, Ismail Onur; Guo, Xin; Morton, Jason; Sturmfels, Bernd 3 2012 Geometry of higher-order Markov chains. Zbl 1347.60103Sturmfels, Bernd 2 2012 Quartic curves and their bitangents. Zbl 1214.14049Plaumann, Daniel; Sturmfels, Bernd; Vinzant, Cynthia 32 2011 Orbitopes. Zbl 1315.52001Sanyal, Raman; Sottile, Frank; Sturmfels, Bernd 28 2011 The convex hull of a variety. Zbl 1253.14055Ranestad, Kristian; Sturmfels, Bernd 14 2011 Tropical quadrics through three points. Zbl 1218.14057Brodsky, Sarah B.; Sturmfels, Bernd 5 2011 Mustafin varieties. Zbl 1248.14013Cartwright, Dustin; Häbich, Mathias; Sturmfels, Bernd; Werner, Annette 5 2011 The algebraic degree of semidefinite programming. Zbl 1184.90119Nie, Jiawang; Ranestad, Kristian; Sturmfels, Bernd 41 2010 Sagbi bases of Cox-Nagata rings. Zbl 1202.14053Sturmfels, Bernd; Xu, Zhiqiang 38 2010 Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Zbl 1440.62255Sturmfels, Bernd; Uhler, Caroline 26 2010 Siphons in chemical reaction networks. Zbl 1198.92020Shiu, Anne; Sturmfels, Bernd 18 2010 Geometry of the restricted Boltzmann machine. Zbl 05777868Cueto, Maria Angélica; Morton, Jason; Sturmfels, Bernd 15 2010 Blow-ups of \(\mathbb{P}^{n-3}\) at \(n\) points and spinor varieties. Zbl 1237.14025Sturmfels, Bernd; Velasco, Mauricio 11 2010 Dualities in convex algebraic geometry. Zbl 1234.90012Rostalski, Philipp; Sturmfels, Bernd 10 2010 The Hilbert scheme of the diagonal in a product of projective spaces. Zbl 1213.14010Cartwright, Dustin; Sturmfels, Bernd 8 2010 Commuting birth-and-death processes. Zbl 1200.60072Evans, Steven N.; Sturmfels, Bernd; Uhler, Caroline 3 2010 Lectures on algebraic statistics. Zbl 1166.13001Drton, Mathias; Sturmfels, Bernd; Sullivant, Seth 95 2009 Toric dynamical systems. Zbl 1188.37082Craciun, Gheorghe; Dickenstein, Alicia; Shiu, Anne; Sturmfels, Bernd 82 2009 Tropical mathematics. Zbl 1227.14051Speyer, David; Sturmfels, Bernd 49 2009 How to draw tropical planes. Zbl 1195.14080Herrmann, Sven; Jensen, Anders; Joswig, Michael; Sturmfels, Bernd 32 2009 Convex rank tests and semigraphoids. Zbl 1198.62038Morton, Jason; Pachter, Lior; Shiu, Anne; Sturmfels, Bernd; Wienand, Oliver 18 2009 Polynomial relations among principal minors of a \(4\times 4\)-matrix. Zbl 1198.14049Lin, Shaowei; Sturmfels, Bernd 11 2009 Open problems in algebraic statistics. Zbl 1158.13300Sturmfels, Bernd 8 2009 Computer algebra in systems biology. Zbl 1229.13027Laubenbacher, Reinhard; Sturmfels, Bernd 8 2009 ...and 171 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,383 Authors 136 Sturmfels, Bernd 36 Hibi, Takayuki 31 Sullivant, Seth 30 Dickenstein, Alicia M. 28 Gaubert, Stéphane 28 Sottile, Frank 27 Takemura, Akimichi 26 Joswig, Michael 26 Michałek, Mateusz 26 Nie, Jiawang 25 Onn, Shmuel 24 Craciun, Gheorghe 24 De Loera, Jesús A. 23 Shitov, Yaroslav Nikolaevich 22 Ohsugi, Hidefumi 21 Bokowski, Jürgen G. 21 Grigor’ev, Dmitriĭ Yur’evich 21 Hauenstein, Jonathan D. 21 Matusevich, Laura Felicia 21 Mohammadi, Fatemeh 21 Villarreal, Rafael Heraclio 20 Santos, Francisco 19 Herzog, Jürgen 19 Kahle, Thomas 19 Markwig, Hannah 19 Qi, Liqun 19 Takayama, Nobuki 19 Thoma, Apostolos 19 Thomas, Rekha R. 18 Manon, Christopher 18 Ottaviani, Giorgio Maria 17 Conca, Aldo 17 Draisma, Jan 17 Ziegler, Günter Matthias 16 Drton, Mathias 16 Emiris, Ioannis Z. 16 Hemmecke, Raymond 16 Izhakian, Zur 16 Mourrain, Bernard 16 Petrović, Sonja 16 Yoshida, Ruriko 15 Aoki, Satoshi 15 D’Andrea, Carlos 15 Gross, Elizabeth 15 Richter-Gebert, Jürgen 15 Varbaro, Matteo 15 Verschelde, Jan 15 Welker, Volkmar 15 Yu, Josephine 14 Ardila, Federico 14 Hoşten, Serkan 14 Nakazato, Hiroshi 14 Padrol, Arnau 14 Römer, Tim 14 Safey El Din, Mohab 14 Sanyal, Raman 14 Vinzant, Cynthia 13 Diaconis, Persi Warren 13 Katthän, Lukas 13 Kummer, Mario Denis 13 Miller, Ezra 13 Morales, Marcel 13 Ojeda Martínez de Castilla, Ignacio 13 Pilaud, Vincent 13 Rodriguez, Jose Israel 12 Bruns, Winfried 12 Chien, Mao-Ting 12 Hà, Huy Tài 12 Johnston, Matthew D. 12 Parrilo, Pablo A. 12 Reiner, Victor 12 Theobald, Thorsten 12 Walther, Uli 11 Allamigeon, Xavier 11 Esterov, Alexander I. 11 Jeronimo, Gabriela 11 Kubjas, Kaie 11 Maclagan, Diane 11 Oeding, Luke 11 Ramírez Alfonsín, Jorge Luis 11 Rapallo, Fabio 11 Rowen, Louis Halle 11 Seiler, Werner M. 11 Sommese, Andrew John 11 Uhler, Caroline 11 Van Tuyl, Adam 11 Weismantel, Robert 10 Delucchi, Emanuele 10 Felsner, Stefan 10 Fink, Alex 10 Fløystad, Gunnar 10 Gaiffi, Giovanni 10 García Sánchez, Pedro A. 10 Jensen, Anders Nedergaard 10 Morrison, Ralph 10 Nagel, Uwe 10 O’Neill, Christopher 10 Proudfoot, Nicholas J. 10 Ranestad, Kristian 10 Rauh, Johannes ...and 4,283 more Authors all top 5 Cited in 521 Serials 254 Journal of Symbolic Computation 210 Journal of Algebra 151 Discrete & Computational Geometry 142 Linear Algebra and its Applications 138 Journal of Pure and Applied Algebra 131 Advances in Mathematics 105 Journal of Combinatorial Theory. 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Série VI 9 SIAM Journal on Applied Dynamical Systems 8 Mathematical Biosciences 8 Nuclear Physics. B 8 Annali di Matematica Pura ed Applicata. Serie Quarta 8 Annals of Mathematics. Second Series ...and 421 more Serials all top 5 Cited in 60 Fields 1,673 Algebraic geometry (14-XX) 1,297 Commutative algebra (13-XX) 981 Combinatorics (05-XX) 825 Convex and discrete geometry (52-XX) 457 Computer science (68-XX) 446 Linear and multilinear algebra; matrix theory (15-XX) 342 Operations research, mathematical programming (90-XX) 324 Numerical analysis (65-XX) 303 Statistics (62-XX) 226 Group theory and generalizations (20-XX) 215 Biology and other natural sciences (92-XX) 208 Associative rings and algebras (16-XX) 165 Number theory (11-XX) 146 Several complex variables and analytic spaces (32-XX) 144 Field theory and polynomials (12-XX) 144 Probability theory and stochastic processes (60-XX) 132 Order, lattices, ordered algebraic structures (06-XX) 109 Dynamical systems and ergodic theory (37-XX) 108 Geometry (51-XX) 97 Quantum theory (81-XX) 89 Ordinary differential equations (34-XX) 87 Manifolds and cell complexes (57-XX) 83 Algebraic topology (55-XX) 81 Special functions (33-XX) 77 Differential geometry (53-XX) 65 Nonassociative rings and algebras (17-XX) 61 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 61 Information and communication theory, circuits (94-XX) 52 Systems theory; control (93-XX) 46 Partial differential equations (35-XX) 41 Operator theory (47-XX) 40 Real functions (26-XX) 40 Functions of a complex variable (30-XX) 39 Statistical mechanics, structure of matter (82-XX) 30 Topological groups, Lie groups (22-XX) 30 Mechanics of particles and systems (70-XX) 27 Category theory; homological algebra (18-XX) 25 Mathematical logic and foundations (03-XX) 24 Global analysis, analysis on manifolds (58-XX) 23 Classical thermodynamics, heat transfer (80-XX) 21 Approximations and expansions (41-XX) 21 General topology (54-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 17 General algebraic systems (08-XX) 17 Calculus of variations and optimal control; optimization (49-XX) 16 General and overarching topics; collections (00-XX) 15 \(K\)-theory (19-XX) 13 Functional analysis (46-XX) 13 Relativity and gravitational theory (83-XX) 12 Difference and functional equations (39-XX) 11 Integral transforms, operational calculus (44-XX) 9 History and biography (01-XX) 9 Mechanics of deformable solids (74-XX) 7 Fluid mechanics (76-XX) 5 Potential theory (31-XX) 4 Integral equations (45-XX) 2 Measure and integration (28-XX) 2 Abstract harmonic analysis (43-XX) 2 Mathematics education (97-XX) 1 Optics, electromagnetic theory (78-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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