Edit Profile (opens in new tab) Sturmfels, Bernd Co-Author Distance Author ID: sturmfels.bernd Published as: Sturmfels, Bernd; Sturmfels, B. Further Spellings: Штрумфельс, Бернд Homepage: https://math.berkeley.edu/~bernd/ External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · Math-Net.Ru · dblp · GND · IdRef · theses.fr Videos: carmin.tv Documents Indexed: 339 Publications since 1986, including 16 Books and 20 Additional arXiv Preprints 11 Contributions as Editor · 1 Further Contribution Software Indexed: 9 Packages Biographic References: 3 Publications Co-Authors: 290 Co-Authors with 305 Joint Publications 6,024 Co-Co-Authors all top 5 Co-Authors 42 single-authored 14 Pachter, Lior 9 Ranestad, Kristian 9 Thomas, Rekha R. 9 Uhler, Caroline 8 Dickenstein, Alicia M. 7 Hoşten, Serkan 6 Bokowski, Jürgen G. 6 De Loera, Jesús A. 6 Morton, Jason 6 Shiu, Anne 6 Sullivant, Seth 5 Agostini, Daniele 5 Billera, Louis J. 5 Cattani, Eduardo H. 5 Eisenbud, David 5 Joswig, Michael 5 Miller, Ezra 5 Ottaviani, Giorgio Maria 5 Peeva, Irena V. 5 Robeva, Elina 5 Sottile, Frank 5 Sverrisdóttir, Svala 5 Takayama, Nobuki 5 Telen, Simon 5 Vinzant, Cynthia 5 Yu, Josephine 5 Zwiernik, Piotr 4 Améndola, Carlos 4 Breiding, Paul 4 Çelik, Türkü Özlüm 4 Drton, Mathias 4 Fevola, Claudia 4 Huggins, Peter 4 Kohn, Kathlén 4 Lin, Shaowei 4 Michałek, Mateusz 4 Nie, Jiawang 4 Panizzut, Marta 4 Ren, Qingchun 4 Richter-Gebert, Jürgen 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 El Maazouz, Yassine 3 Eriksson, Nicholas 3 Gritzmann, Peter 3 Huber, Birkett 3 Kahle, Thomas 3 Kapranov, Mikhail M. 3 Kileel, Joe 3 Kleinschmidt, Peter 3 Kummer, Mario Denis 3 Laubenbacher, Reinhard C. 3 Mira, Portia M. 3 Onn, Shmuel 3 Parrilo, Pablo A. 3 Plaumann, Daniel 3 Rostalski, Philipp 3 Sattelberger, Anna-Laura 3 Speyer, David E. 3 Stillman, Michael Eugene 3 Wienand, Oliver 2 Agarwal, Sameer 2 Anas Hahn, Marvin 2 Avramov, Luchezar L. 2 Björner, Anders 2 Boege, Tobias 2 Brodsky, Sarah B. 2 Brysiewicz, Taylor 2 Cid-Ruiz, Yairon 2 Cifuentes, Diego 2 Crona, Kristina 2 Cueto, María Angélica 2 Develin, Mike 2 Di Rocco, Sandra 2 Draisma, Jan 2 Early, Nicholas 2 Feichtner, Eva Maria 2 Friedman, Hannah 2 Fulton, William 2 Geiger, Alheydis 2 Green, Mark Lee 2 Greene, Devin C. V. 2 Härkönen, Marc 2 Hauenstein, Jonathan D. 2 Hemmecke, Raymond 2 Horobeţ, Emil 2 Huneke, Craig L. 2 Jamneshan, Asgar 2 Jensen, Anders Nedergaard 2 Kaihnsa, Nidhi 2 Khetan, Amit 2 Kubjas, Kaie ...and 192 more Co-Authors all top 5 Serials 18 Journal of Symbolic Computation 11 Discrete & Computational Geometry 9 Journal of Algebra 8 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 Experimental Mathematics 4 Advances in Geometry 4 Journal of Algebraic Statistics 4 Algebraic Statistics 3 American Mathematical Monthly 3 Mathematics of Computation 3 Beiträge zur Algebra und Geometrie 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 IMRN. International Mathematics Research Notices 3 Journal of Algebraic Combinatorics 3 Documenta Mathematica 2 Discrete Mathematics 2 Acta Mathematica Vietnamica 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 Proceedings of the National Academy of Sciences of the United States of America 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 Oberwolfach Seminars 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 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 Glasgow Mathematical Journal 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 Rendiconti dell’Istituto di Matematica dell’Università di Trieste 1 Results in Mathematics 1 Revista de la Unión Matemática Argentina 1 SIAM Journal on Numerical Analysis 1 SIGSAM Bulletin 1 Tôhoku 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 Journal of Lie Theory 1 Selecta Mathematica. New Series 1 Statistica Sinica ...and 31 more Serials all top 5 Fields 180 Algebraic geometry (14-XX) 129 Commutative algebra (13-XX) 79 Convex and discrete geometry (52-XX) 67 Combinatorics (05-XX) 62 Computer science (68-XX) 51 Statistics (62-XX) 36 Operations research, mathematical programming (90-XX) 29 Linear and multilinear algebra; matrix theory (15-XX) 27 Numerical analysis (65-XX) 23 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) 8 Associative rings and algebras (16-XX) 8 Group theory and generalizations (20-XX) 7 Dynamical systems and ergodic theory (37-XX) 5 Nonassociative rings and algebras (17-XX) 5 Partial differential equations (35-XX) 5 Algebraic topology (55-XX) 4 History and biography (01-XX) 4 Differential geometry (53-XX) 4 Information and communication theory, circuits (94-XX) 3 Number theory (11-XX) 3 Functions of a complex variable (30-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 Calculus of variations and optimal control; optimization (49-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-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 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 301 Publications have been cited 10,509 times in 6,292 Documents Cited by ▼ Year ▼ Gröbner bases and convex polytopes. Zbl 0856.13020 Sturmfels, Bernd 677 1996 Combinatorial commutative algebra. Zbl 1090.13001 Miller, Ezra; Sturmfels, Bernd 527 2005 Introduction to tropical geometry. Zbl 1321.14048 Maclagan, Diane; Sturmfels, Bernd 470 2015 Solving systems of polynomial equations. Zbl 1101.13040 Sturmfels, Bernd 313 2002 Oriented matroids. 2nd ed. Zbl 0944.52006 Björner, Anders; Las Vergnas, Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter 308 1999 Algebraic algorithms for sampling from conditional distributions. Zbl 0952.62088 Diaconis, Persi; Sturmfels, Bernd 231 1998 The tropical Grassmannian. Zbl 1065.14071 Speyer, David; Sturmfels, Bernd 219 2004 Binomial ideals. Zbl 0873.13021 Eisenbud, David; Sturmfels, Bernd 207 1996 Oriented matroids. Zbl 0773.52001 Björner, Anders; Las Vergnas, Michel; Sturmfels, Bernd; White, Neil; Ziegler, Günter M. 205 1993 Algorithms in invariant theory. Zbl 0802.13002 Sturmfels, Bernd 193 1993 Gröbner deformations of hypergeometric differential equations. Zbl 0946.13021 Saito, Mutsumi; Sturmfels, Bernd; Takayama, Nobuki 189 2000 Algebraic statistics for computational biology. Zbl 1108.62118 162 2005 First steps in tropical geometry. Zbl 1093.14080 Richter-Gebert, Jürgen; Sturmfels, Bernd; Theobald, Thorsten 155 2005 Tropical convexity. Zbl 1054.52004 Develin, Mike; Sturmfels, Bernd 153 2004 Lectures on algebraic statistics. Zbl 1166.13001 Drton, Mathias; Sturmfels, Bernd; Sullivant, Seth 144 2009 Algorithms in invariant theory. 2nd ed. Zbl 1154.13003 Sturmfels, Bernd 137 2008 Matroid polytopes, nested sets and Bergman fans. Zbl 1092.52006 Feichtner, Eva Maria; Sturmfels, Bernd 126 2005 A polyhedral method for solving sparse polynomial systems. Zbl 0849.65030 Huber, Birkett; Sturmfels, Bernd 123 1995 Combinatorial commutative algebra. Zbl 1066.13001 Miller, Ezra; Sturmfels, Bernd 122 2005 Intersection theory on toric varieties. Zbl 0885.14025 Fulton, William; Sturmfels, Bernd 111 1997 Toric dynamical systems. Zbl 1188.37082 Craciun, Gheorghe; Dickenstein, Alicia; Shiu, Anne; Sturmfels, Bernd 106 2009 The number of eigenvalues of a tensor. Zbl 1277.15007 Cartwright, Dustin; Sturmfels, Bernd 106 2013 Minimizing polynomial functions. Zbl 1099.13516 Parrilo, Pablo A.; Sturmfels, Bernd 101 2003 Fiber polytopes. Zbl 0762.52003 Billera, Louis J.; Sturmfels, Bernd 97 1992 Monomial resolutions. Zbl 0909.13010 Bayer, Dave; Peeva, Irena; Sturmfels, Bernd 96 1998 Cellular resolutions of monomial modules. Zbl 0909.13011 Bayer, Dave; Sturmfels, Bernd 95 1998 On the Newton polytope of the resultant. Zbl 0798.05074 Sturmfels, Bernd 93 1994 The Euclidean distance degree of an algebraic variety. Zbl 1370.51020 Draisma, Jan; Horobeţ, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha R. 89 2016 Minimizing polynomials via sum of squares over the gradient ideal. Zbl 1134.90032 Nie, Jiawang; Demmel, James; Sturmfels, Bernd 81 2006 Computing tropical varieties. Zbl 1121.14051 Bogart, T.; Jensen, A. N.; Speyer, D.; Sturmfels, B.; Thomas, R. R. 79 2007 On the rank of a tropical matrix. Zbl 1095.15001 Develin, Mike; Santos, Francisco; Sturmfels, Bernd 78 2005 On the toric algebra of graphical models. Zbl 1104.60007 Geiger, Dan; Meek, Christopher; Sturmfels, Bernd 74 2006 Computational synthetic geometry. Zbl 0683.05015 Bokowski, Jürgen; Sturmfels, Bernd 69 1989 Constructions and complexity of secondary polytopes. Zbl 0714.52004 Billera, Louis J.; Filliman, Paul; Sturmfels, Bernd 67 1990 Tropical mathematics. Zbl 1227.14051 Speyer, David; Sturmfels, Bernd 65 2009 Multigraded Hilbert schemes. Zbl 1072.14007 Haiman, Mark; Sturmfels, Bernd 65 2004 Algebraic geometry of Bayesian networks. Zbl 1126.68102 Garcia, Luis David; Stillman, Michael; Sturmfels, Bernd 63 2005 Toric ideals of phylogenetic invariants. Zbl 1391.13058 Sturmfels, Bernd; Sullivant, Seth 62 2005 Tropical discriminants. Zbl 1166.14033 Dickenstein, Alicia; Feichtner, Eva Maria; Sturmfels, Bernd 60 2007 Minkowski addition of polytopes: Computational complexity and applications to Gröbner bases. Zbl 0798.68157 Gritzmann, Peter; Sturmfels, Bernd 59 1993 Intersection theory on spherical varieties. Zbl 0819.14019 Fulton, William; MacPherson, Robert; Sottile, F.; Sturmfels, Bernd 58 1995 The algebraic degree of semidefinite programming. Zbl 1184.90119 Nie, Jiawang; Ranestad, Kristian; Sturmfels, Bernd 56 2010 The maximum likelihood degree. Zbl 1123.13019 Catanese, Fabrizio; Hoşten, Serkan; Khetan, Amit; Sturmfels, Bernd 55 2006 Orbitopes. Zbl 1315.52001 Sanyal, Raman; Sottile, Frank; Sturmfels, Bernd 53 2011 Chow polytopes and general resultants. Zbl 0780.14027 Kapranov, M. M.; Sturmfels, Bernd; Zelevinsky, Andrei V. 53 1992 Gröbner bases and Stanley decompositions of determinantal ideals. Zbl 0685.13005 Sturmfels, Bernd 53 1990 Invitation to nonlinear algebra. Zbl 1477.14001 Michałek, Mateusz; Sturmfels, Bernd 50 2021 Maximal minors and their leading terms. Zbl 0776.13009 Sturmfels, Bernd; Zelevinsky, Andrei V. 50 1993 How to draw tropical planes. Zbl 1195.14080 Herrmann, Sven; Jensen, Anders; Joswig, Michael; Sturmfels, Bernd 49 2009 Syzygies of codimension 2 lattice ideals. Zbl 0918.13006 Peeva, Irena; Sturmfels, Bernd 49 1998 Product formulas for resultants and Chow forms. Zbl 0792.13006 Pedersen, Paul; Sturmfels, Bernd 49 1993 Elimination theory for tropical varieties. Zbl 1157.14038 Sturmfels, Bernd; Tevelev, Jenia 47 2008 Gröbner bases of toric varieties. Zbl 0714.14034 Sturmfels, Bernd 44 1991 Toric hyperkähler varieties. Zbl 1029.53054 Hausel, Tamás; Sturmfels, Bernd 43 2002 Sagbi bases of Cox-Nagata rings. Zbl 1202.14053 Sturmfels, Bernd; Xu, Zhiqiang 42 2010 Likelihood geometry. Zbl 1328.14004 Huh, June; Sturmfels, Bernd 42 2014 On vector partition functions. Zbl 0837.11055 Sturmfels, Bernd 42 1995 Bounds on degrees of projective schemes. Zbl 0828.14040 Sturmfels, Bernd; Ngô Viêt Trung; Vogel, Wolfgang 41 1995 Quotients of toric varieties. Zbl 0762.14023 Kapranov, M. M.; Sturmfels, Bernd; Zelevinsky, Andrei V. 41 1991 Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry. Zbl 1440.62255 Sturmfels, Bernd; Uhler, Caroline 40 2010 Cellular strings on polytopes. Zbl 0812.52007 Billera, Louis J.; Kapranov, M. M.; Sturmfels, Bernd 40 1994 Quartic curves and their bitangents. Zbl 1214.14049 Plaumann, Daniel; Sturmfels, Bernd; Vinzant, Cynthia 39 2011 Generic lattice ideals. Zbl 0905.13005 Peeva, Irena; Sturmfels, Bernd 39 1998 Variation of cost functions in integer programming. Zbl 0888.90125 Sturmfels, Bernd; Thomas, Rekha R. 38 1997 Equations defining toric varieties. Zbl 0914.14022 Sturmfels, Bernd 38 1997 Solving the likelihood equations. Zbl 1097.13035 Hosten, Serkan; Khetan, Amit; Sturmfels, Bernd 35 2005 Computing linear matrix representations of Helton-Vinnikov curves. Zbl 1328.14093 Plaumann, Daniel; Sturmfels, Bernd; Vinzant, Cynthia 35 2012 Generic and cogeneric monomial ideals. Zbl 0955.13008 Miller, Ezra; Sturmfels, Bernd; Yanagawa, Kohji 35 2000 Syzygies of oriented matroids. Zbl 1022.13002 Novik, Isabella; Postnikov, Alexander; Sturmfels, Bernd 35 2002 Sparse elimination theory. Zbl 0837.13011 Sturmfels, Bernd 35 1993 Tropical geometry of statistical models. Zbl 1135.62302 Pachter, Lior; Sturmfels, Bernd 35 2004 Algorithms for the Quillen-Suslin theorem. Zbl 0747.13020 Logar, Alessandro; Sturmfels, Bernd 35 1992 Combinatorial secant varieties. Zbl 1107.14045 Sturmfels, Bernd; Sullivant, Seth 34 2006 Affine buildings and tropical convexity. Zbl 1133.52003 Joswig, Michael; Sturmfels, Bernd; Yu, Josephine 34 2007 Lattice walks and primary decomposition. Zbl 0962.05010 Diaconis, Persi; Eisenbud, David; Sturmfels, Bernd 34 1998 Hyperdeterminantal relations among symmetric principal minors. Zbl 1130.15005 Holtz, Olga; Sturmfels, Bernd 34 2007 Higher Lawrence configurations. Zbl 1036.52018 Santos, Francisco; Sturmfels, Bernd 33 2003 Computing Hopf bifurcations. I. Zbl 0948.37037 Guckenheimer, John; Myers, Mark; Sturmfels, Bernd 33 1997 Polynomial equations and convex polytopes. Zbl 0988.52021 Sturmfels, Bernd 32 1998 A Hilbert scheme in computer vision. Zbl 1284.13035 Aholt, Chris; Sturmfels, Bernd; Thomas, Rekha 31 2013 Four counterexamples in combinatorial algebraic geometry. Zbl 1018.14022 Sturmfels, Bernd 31 2000 Extension spaces of oriented matroids. Zbl 0783.52009 Sturmfels, Bernd; Ziegler, Günter M. 31 1993 Computing combinatorial decompositions of rings. Zbl 0739.68051 Sturmfels, Bernd; White, Neil 31 1991 Initial complexes of prime ideals. Zbl 0877.13025 Kalkbrener, Michael; Sturmfels, Bernd 30 1995 Algebraic factor analysis: tetrads, pentads and beyond. Zbl 1111.13020 Drton, Mathias; Sturmfels, Bernd; Sullivant, Seth 30 2007 Algebraic boundaries of Hilbert’s SOS cones. Zbl 1273.13043 Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd 29 2012 Multigraded resultants of Sylvester type. Zbl 0813.13018 Sturmfels, Bernd; Zelevinsky, Andrei V. 29 1994 Residues and resultants. Zbl 0933.14033 Cattani, Eduardo; Dickenstein, Alicia; Sturmfels, Bernd 29 1998 Phylogenetic algebraic geometry. Zbl 1106.14050 Eriksson, Nicholas; Ranestad, Kristian; Sturmfels, Bernd; Sullivant, Seth 28 2005 Convex rank tests and semigraphoids. Zbl 1198.62038 Morton, Jason; Pachter, Lior; Shiu, Anne; Sturmfels, Bernd; Wienand, Oliver 27 2009 Algebraic systems biology: a case study for the Wnt pathway. Zbl 1356.92038 Gross, Elizabeth; Harrington, Heather A.; Rosen, Zvi; Sturmfels, Bernd 27 2016 Toric geometry of cuts and splits. Zbl 1180.13040 Sturmfels, Bernd; Sullivant, Seth 26 2008 The hyperdeterminant and triangulations of the 4-cube. Zbl 1194.52016 Huggins, Peter; Sturmfels, Bernd; Yu, Josephine; Yuster, Debbie S. 26 2008 How to shell a monoid. Zbl 0893.20048 Peeva, Irena; Reiner, Victor; Sturmfels, Bernd 26 1998 Exponential varieties. Zbl 1345.14048 Michałek, Mateusz; Sturmfels, Bernd; Uhler, Caroline; Zwiernik, Piotr 25 2016 Exact solutions in structured low-rank approximation. Zbl 1318.14057 Ottaviani, Giorgio; Spaenlehauer, Pierre-Jean; Sturmfels, Bernd 25 2014 Moduli of tropical plane curves. Zbl 1349.14043 Brodsky, Sarah; Joswig, Michael; Morrison, Ralph; Sturmfels, Bernd 24 2015 Computing multidimensional residues. Zbl 0882.13020 Cattani, E.; Dickenstein, A.; Sturmfels, Bernd 24 1996 Gröbner bases of lattices, corner polyhedra, and integer programming. Zbl 0863.90115 Sturmfels, Bernd; Weismantel, Robert; Ziegler, Günter M. 24 1995 Cutting corners. Zbl 0955.52008 Onn, Shmuel; Sturmfels, Bernd 23 1999 Likelihood geometry of determinantal point processes. Zbl 07836978 Friedman, Hannah; Sturmfels, Bernd; Zubkov, Maksym 1 2024 Likelihood degenerations. Zbl 1535.14106 Agostini, Daniele; Brysiewicz, Taylor; Fevola, Claudia; Kühne, Lukas; Sturmfels, Bernd; Telen, Simon 9 2023 KP solitons from tropical limits. Zbl 1495.14046 Agostini, Daniele; Fevola, Claudia; Mandelshtam, Yelena; Sturmfels, Bernd 7 2023 Linear PDE with constant coefficients. Zbl 1514.13026 Ait El Manssour, Rida; Härkönen, Marc; Sturmfels, Bernd 7 2023 Primary decomposition with differential operators. Zbl 1524.13078 Cid-Ruiz, Yairon; Sturmfels, Bernd 3 2023 Making waves. Zbl 1523.35123 Härkönen, Marc; Hirsch, Jonas; Sturmfels, Bernd 2 2023 Moment varieties for mixtures of products. Zbl 07760747 Alexandr, Yulia; Kileel, Joe; Sturmfels, Bernd 1 2023 Geometry of dependency equilibria. Zbl 1518.14003 Portakal, Irem; Sturmfels, Bernd 5 2022 Voronoi cells of varieties. Zbl 1477.13054 Cifuentes, Diego; Ranestad, Kristian; Sturmfels, Bernd; Weinstein, Madeleine 3 2022 Positivity certificates via integral representations. Zbl 1492.14107 Kozhasov, Khazhgali; Michałek, Mateusz; Sturmfels, Bernd 2 2022 Orders and polytropes: matrix algebras from valuations. Zbl 1502.14149 El Maazouz, Yassine; Hahn, Marvin Anas; Nebe, Gabriele; Stanojkovski, Mima; Sturmfels, Bernd 2 2022 Invitation to nonlinear algebra. Zbl 1477.14001 Michałek, Mateusz; Sturmfels, Bernd 50 2021 Likelihood equations and scattering amplitudes. Zbl 1515.62137 Sturmfels, Bernd; Telen, Simon 15 2021 Primary ideals and their differential equations. Zbl 1511.13027 Cid-Ruiz, Yairon; Homs, Roser; Sturmfels, Bernd 13 2021 Wasserstein distance to independence models. Zbl 1460.62205 Çelik, Türkü Özlüm; Jamneshan, Asgar; Montúfar, Guido; Sturmfels, Bernd; Venturello, Lorenzo 11 2021 Discrete statistical models with rational maximum likelihood estimator. Zbl 1465.62184 Duarte, Eliana; Marigliano, Orlando; Sturmfels, Bernd 10 2021 Pencils of quadrics: old and new. Zbl 1480.14037 Fevola, C.; Mandelshtam, Y.; Sturmfels, B. 8 2021 Maximum likelihood estimation for totally positive log-concave densities. Zbl 1473.62048 Robeva, Elina; Sturmfels, Bernd; Tran, Ngoc; Uhler, Caroline 4 2021 The Dubrovin threefold of an algebraic curve. Zbl 1465.14036 Agostini, Daniele; Çelik, Türkü Özlüm; Sturmfels, Bernd 4 2021 Tangent quadrics in real 3-space. Zbl 1481.14082 Brysiewicz, T.; Fevola, C.; Sturmfels, B. 3 2021 Bad projections of the PSD cone. Zbl 1467.14120 Jiang, Yuhan; Sturmfels, Bernd 3 2021 Jordan algebras of symmetric matrices. Zbl 1519.17034 Bik, A.; Eisenmann, H.; Sturmfels, B. 2 2021 Theta surfaces. Zbl 1468.14080 Agostini, Daniele; Çelik, Türkü Özlüm; Struwe, Julia; Sturmfels, Bernd 2 2021 Estimating linear covariance models with numerical nonlinear algebra. Zbl 1461.62230 Sturmfels, Bernd; Timme, Sascha; Zwiernik, Piotr 15 2020 An octanomial model for cubic surfaces. Zbl 1451.14116 Panizzut, Marta; Sertöz, Emre; Sturmfels, Bernd 10 2020 Twenty-seven questions about the cubic surface. Zbl 1454.14104 Ranestad, Kristian; Sturmfels, Bernd 9 2020 The Schläfli fan. Zbl 1505.14128 Joswig, Michael; Panizzut, Marta; Sturmfels, Bernd 8 2020 3264 conics in a second. Zbl 1437.14053 Breiding, Paul; Sturmfels, Bernd; Timme, Sascha 7 2020 The geometry of SDP-exactness in quadratic optimization. Zbl 1445.90075 Cifuentes, Diego; Harris, Corey; Sturmfels, Bernd 7 2020 Optimal transport to a variety. Zbl 07441083 Çelik, Türkü Özlüm; Jamneshan, Asgar; Montúfar, Guido; Sturmfels, Bernd; Venturello, Lorenzo 5 2020 Moment varieties of measures on polytopes. Zbl 1506.13047 Kohn, Kathlén; Shapiro, Boris; Sturmfels, Bernd 5 2020 Brownian motion tree models are toric. Zbl 1538.62361 Sturmfels, Bernd; Uhler, Caroline; Zwiernik, Piotr 4 2020 Algebraic analysis of rotation data. Zbl 1461.62220 Adamer, Michael F.; Lőrincz, András C.; Sattelberger, Anna-Laura; Sturmfels, Bernd 2 2020 Varieties of signature tensors. Zbl 1411.14068 Améndola, Carlos; Friz, Peter; Sturmfels, Bernd 14 2019 The geometry of gaussoids. Zbl 1453.13076 Boege, Tobias; D’Alì, Alessio; Kahle, Thomas; Sturmfels, Bernd 11 2019 Learning paths from signature tensors. Zbl 1469.14116 Pfeffer, Max; Seigal, Anna; Sturmfels, Bernd 10 2019 Schottky algorithms: classical meets tropical. Zbl 1505.14071 Chua, Lynn; Kummer, Mario; Sturmfels, Bernd 8 2019 Geometry of log-concave density estimation. Zbl 1416.62202 Robeva, Elina; Sturmfels, Bernd; Uhler, Caroline 5 2019 Computing convex hulls of trajectories. Zbl 07149412 Ciripoi, Daniel; Kaihnsa, Nidhi; Löhne, Andreas; Sturmfels, Bernd 4 2019 Sixty-four curves of degree six. Zbl 1440.14270 Kaihnsa, Nidhi; Kummer, Mario; Plaumann, Daniel; Namin, Mahsa Sayyary; Sturmfels, Bernd 3 2019 Learning algebraic varieties from samples. Zbl 1481.13040 Breiding, Paul; Kališnik, Sara; Sturmfels, Bernd; Weinstein, Madeleine 23 2018 Algebraic identifiability of Gaussian mixtures. Zbl 1423.14284 Améndola, Carlos; Ranestad, Kristian; Sturmfels, Bernd 13 2018 Nearest points on toric varieties. Zbl 1393.14049 Helmer, Martin; Sturmfels, Bernd 9 2018 Real space sextics and their tritangents. Zbl 1467.14148 Kulkarni, Avinash; Ren, Yue; Sayyary Namin, Mahsa; Sturmfels, Bernd 5 2018 Distortion varieties. Zbl 1408.14191 Kileel, Joe; Kukelova, Zuzana; Pajdla, Tomas; Sturmfels, Bernd 3 2018 Changing views on curves and surfaces. Zbl 1388.14160 Kohn, Kathlén; Sturmfels, Bernd; Trager, Matthew 2 2018 Convexity in tree spaces. Zbl 1370.05040 Lin, Bo; Sturmfels, Bernd; Tang, Xiaoxian; Yoshida, Ruriko 21 2017 Eigenconfigurations of tensors. Zbl 1360.15011 Abo, Hirotachi; Seigal, Anna; Sturmfels, Bernd 21 2017 The Hurwitz form of a projective variety. Zbl 1359.14043 Sturmfels, Bernd 20 2017 Real rank geometry of ternary forms. Zbl 1390.14179 Michałek, Mateusz; Moon, Hyunsuk; Sturmfels, Bernd; Ventura, Emanuele 18 2017 Real rank two geometry. Zbl 1401.14229 Seigal, Anna; Sturmfels, Bernd 7 2017 Congruences and concurrent lines in multi-view geometry. Zbl 1367.14022 Ponce, Jean; Sturmfels, Bernd; Trager, Mathew 7 2017 On the existence of epipolar matrices. Zbl 1458.68222 Agarwal, Sameer; Lee, Hon-Leung; Sturmfels, Bernd; Thomas, Rekha R. 7 2017 How to flatten a soccer ball. Zbl 1406.14042 Kubjas, Kaie; Parrilo, Pablo A.; Sturmfels, Bernd 4 2017 Combinatorial algebraic geometry. Selected papers from the 2016 apprenticeship program, Ottawa, Canada, July–December 2016. Zbl 1387.14014 1 2017 Does antibiotic resistance evolve in hospitals? Zbl 1373.92067 Seigal, Anna; Mira, Portia; Sturmfels, Bernd; Barlow, Miriam 1 2017 The Euclidean distance degree of an algebraic variety. Zbl 1370.51020 Draisma, Jan; Horobeţ, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha R. 89 2016 Algebraic systems biology: a case study for the Wnt pathway. Zbl 1356.92038 Gross, Elizabeth; Harrington, Heather A.; Rosen, Zvi; Sturmfels, Bernd 27 2016 Exponential varieties. Zbl 1345.14048 Michałek, Mateusz; Sturmfels, Bernd; Uhler, Caroline; Zwiernik, Piotr 25 2016 Moment varieties of Gaussian mixtures. Zbl 1361.13017 Améndola, Carlos; Faugère, Jean-Charles; Sturmfels, Bernd 17 2016 Tensors and their eigenvectors. Zbl 1352.15030 Sturmfels, Bernd 13 2016 Duality of multiple root loci. Zbl 1346.14126 Lee, Hwangrae; Sturmfels, Bernd 12 2016 Tropicalization of del Pezzo surfaces. Zbl 1375.14218 Ren, Qingchun; Shaw, Kristin; Sturmfels, Bernd 12 2016 Decomposing tensors into frames. Zbl 1331.15019 Oeding, Luke; Robeva, Elina; Sturmfels, Bernd 8 2016 Symmetric matrices, Catalan paths, and correlations. Zbl 1344.05042 Sturmfels, Bernd; Tsukerman, Emmanuel; Williams, Lauren 3 2016 Computing the Chow variety of quadratic space curves. Zbl 1460.14132 Bürgisser, Peter; Kohn, Kathlén; Lairez, Pierre; Sturmfels, Bernd 2 2016 Maximum likelihood estimates for Gaussian mixtures are transcendental. Zbl 1460.62081 Améndola, Carlos; Drton, Mathias; Sturmfels, Bernd 2 2016 Rigid multiview varieties. Zbl 1360.13063 Joswig, Michael; Kileel, Joe; Sturmfels, Bernd; Wagner, André 1 2016 Introduction to tropical geometry. Zbl 1321.14048 Maclagan, Diane; Sturmfels, Bernd 470 2015 Moduli of tropical plane curves. Zbl 1349.14043 Brodsky, Sarah; Joswig, Michael; Morrison, Ralph; Sturmfels, Bernd 24 2015 Fixed points of the EM algorithm and nonnegative rank boundaries. Zbl 1308.62035 Kubjas, Kaie; Robeva, Elina; Sturmfels, Bernd 17 2015 Quartic spectrahedra. Zbl 1328.14091 Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd; Vinzant, Cynthia 17 2015 A family of quasisymmetry models. Zbl 1344.05155 Kateri, Maria; Mohammadi, Fatemeh; Sturmfels, Bernd 13 2015 Tensors of nonnegative rank two. Zbl 1312.15033 Allman, Elizabeth S.; Rhodes, John A.; Sturmfels, Bernd; Zwiernik, Piotr 12 2015 Generic spectrahedral shadows. Zbl 1346.14132 Sinn, Rainer; Sturmfels, Bernd 9 2015 Cayley-Bacharach formulas. Zbl 1346.14083 Ren, Qingchun; Richter-Gebert, Jürgen; Sturmfels, Bernd 6 2015 Rational design of antibiotic treatment plans: a treatment strategy for managing evolution and reversing resistance. Zbl 1375.92032 Mira, Portia M.; Crona, Kristina; Greene, Devin; Meza, Juan C.; Sturmfels, Bernd; Barlow, Miriam 4 2015 Correction: “Rational design of antibiotic treatment plans: a treatment strategy for managing evolution and reversing resistance”. Zbl 1376.92025 Mira, Portia M.; Crona, Kristina; Greene, Devin; Meza, Juan C.; Sturmfels, Bernd; Barlow, Miriam 2 2015 Likelihood geometry. Zbl 1328.14004 Huh, June; Sturmfels, Bernd 42 2014 Exact solutions in structured low-rank approximation. Zbl 1318.14057 Ottaviani, Giorgio; Spaenlehauer, Pierre-Jean; Sturmfels, Bernd 25 2014 Maximum likelihood for matrices with rank constraints. Zbl 1345.62043 Hauenstein, Jonathan; Rodriguez, Jose Israel; Sturmfels, Bernd 19 2014 Tropicalization of classical moduli spaces. Zbl 1305.14031 Ren, Qingchun; Sam, Steven V.; Sturmfels, Bernd 13 2014 Hypersurfaces and their singularities in partial correlation testing. Zbl 1308.62110 Lin, Shaowei; Uhler, Caroline; Sturmfels, Bernd; Bühlmann, Peter 5 2014 The Euclidean distance degree. Zbl 1346.68281 Draisma, Jan; Horobeţ, Emil; Ottaviani, Giorgio; Sturmfels, Bernd; Thomas, Rekha 3 2014 Combinatorial algebraic geometry. Lecture notes of the CIME-CIRM summer school, Levico Terme, Italy, June 10–15, 2013. Zbl 1290.14001 1 2014 The number of eigenvalues of a tensor. Zbl 1277.15007 Cartwright, Dustin; Sturmfels, Bernd 106 2013 A Hilbert scheme in computer vision. Zbl 1284.13035 Aholt, Chris; Sturmfels, Bernd; Thomas, Rekha 31 2013 The entropic discriminant. Zbl 1284.15006 Sanyal, Raman; Sturmfels, Bernd; Vinzant, Cynthia 21 2013 Mixed discriminants. Zbl 1273.13051 Cattani, Eduardo; Cueto, María Angélica; Dickenstein, Alicia; Di Rocco, Sandra; Sturmfels, Bernd 18 2013 Monomials, binomials and Riemann-Roch. Zbl 1272.13017 Manjunath, Madhusudan; Sturmfels, Bernd 14 2013 The universal Kummer threefold. Zbl 1312.14103 Ren, Qingchun; Sam, Steven V.; Schrader, Gus; Sturmfels, Bernd 13 2013 Binary cumulant varieties. Zbl 1274.13048 Sturmfels, Bernd; Zwiernik, Piotr 13 2013 Dualities. Zbl 1360.90195 Rostalski, Philipp; Sturmfels, Bernd 11 2013 Elliptic curves in honeycomb form. Zbl 1312.14142 Chan, Melody; Sturmfels, Bernd 10 2013 Matrices with eigenvectors in a given subspace. Zbl 1272.15010 Ottaviani, Giorgio; Sturmfels, Bernd 8 2013 Combinatorial types of tropical eigenvectors. Zbl 1269.15009 Sturmfels, Bernd; Tran, Ngoc Mai 6 2013 Toric cubes. Zbl 1315.52011 Engström, Alexander; Hersh, Patricia; Sturmfels, Bernd 4 2013 Capacity pre-log of noncoherent SIMO channels via Hironaka’s theorem. Zbl 1364.94430 Morgenshtern, 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 1328.14093 Plaumann, Daniel; Sturmfels, Bernd; Vinzant, Cynthia 35 2012 Algebraic boundaries of Hilbert’s SOS cones. Zbl 1273.13043 Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd 29 2012 ...and 201 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 6,040 Authors 164 Sturmfels, Bernd 44 Hibi, Takayuki 41 Michałek, Mateusz 37 Joswig, Michael 36 Dickenstein, Alicia M. 36 Gaubert, Stéphane 35 Sottile, Frank 34 De Loera, Jesús A. 34 Sullivant, Seth 31 Craciun, Gheorghe 30 Mohammadi, Fatemeh 30 Onn, Shmuel 29 Nie, Jiawang 28 Thomas, Rekha R. 27 Bokowski, Jürgen G. 27 Ohsugi, Hidefumi 27 Safey El Din, Mohab 27 Takemura, Akimichi 26 Conca, Aldo 26 Grigor’ev, Dmitriĭ Yur’evich 26 Villarreal, Rafael Heraclio 25 Emiris, Ioannis Z. 25 Hauenstein, Jonathan D. 25 Markwig, Hannah 25 Rodriguez, Jose Israel 25 Shitov, Yaroslav Nikolaevich 24 Kahle, Thomas 24 Matusevich, Laura Felicia 24 Yoshida, Ruriko 23 Herzog, Jürgen 23 Mourrain, Bernard 23 Ottaviani, Giorgio Maria 23 Santos, Francisco 23 Takayama, Nobuki 23 Thoma, Apostolos 22 Draisma, Jan 22 Manon, Christopher 21 Knauer, Kolja B. 21 Qi, Liqun 20 Gross, Elizabeth 20 Petrović, Sonja 20 Römer, Tim 19 Breiding, Paul 19 Drton, Mathias 19 Padrol, Arnau 19 Sanyal, Raman 18 Ardila, Federico 18 D’Andrea, Carlos 18 Kummer, Mario Denis 18 Leykin, Anton 18 Parrilo, Pablo A. 18 Pilaud, Vincent 18 Welker, Volkmar 18 Ziegler, Günter Matthias 17 Aoki, Satoshi 17 Cid-Ruiz, Yairon 17 Izhakian, Zur 17 Miller, Ezra 17 Ramírez Alfonsín, Jorge Luis 17 Varbaro, Matteo 17 Verschelde, Jan 17 Walther, Uli 16 Améndola, Carlos 16 Diaconis, Persi Warren 16 Eur, Christopher 16 Hemmecke, Raymond 16 Hoşten, Serkan 16 Katthän, Lukas 16 Maclagan, Diane 16 Ojeda Martínez de Castilla, Ignacio 16 Vinzant, Cynthia 16 Yu, Josephine 15 Delucchi, Emanuele 15 Faugère, Jean-Charles 15 Kubjas, Kaie 15 Nakazato, Hiroshi 15 Richter-Gebert, Jürgen 15 Shiu, Anne 15 Telen, Simon 15 Tsigaridas, Elias P. 14 Bruns, Winfried 14 Felsner, Stefan 14 Rapallo, Fabio 14 Reiner, Victor 14 Rowen, Louis Halle 14 Seigal, Anna Leah 14 Theobald, Thorsten 14 Van Tuyl, Adam 13 Allamigeon, Xavier 13 Chien, Mao-Ting 13 Di Rocco, Sandra 13 Fink, Alex 13 Fløystad, Gunnar 13 Hà, Huy Tài 13 Huh, June 13 Katsabekis, Anargyros 13 Krivulin, Nikolai K. 13 Lin, Kuei-Nuan 13 Mirò-Roig, Rosa Maria 13 Morales, Marcel ...and 5,940 more Authors all top 5 Cited in 628 Serials 315 Journal of Symbolic Computation 253 Journal of Algebra 189 Journal of Pure and Applied Algebra 188 Discrete & Computational Geometry 168 Linear Algebra and its Applications 163 Advances in Mathematics 118 Journal of Algebraic Combinatorics 114 Journal of Combinatorial Theory. 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New Series 16 Journal of Algebraic Geometry 15 Geometriae Dedicata 15 Journal of Multivariate Analysis 15 Mathematika 15 Combinatorica 15 International Journal of Mathematics 15 Vietnam Journal of Mathematics 15 Arnold Mathematical Journal 14 Acta Mathematica Vietnamica 14 Bulletin of the London Mathematical Society 14 Compositio Mathematica 14 Kybernetika 14 Journal of Physics A: Mathematical and Theoretical 14 Electronic Journal of Statistics 13 Automatica 13 Journal of Optimization Theory and Applications 13 Topology and its Applications 13 Journal of Complexity 13 Computational Optimization and Applications 13 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 SIAM Journal on Applied Dynamical Systems 13 Proceedings of the Steklov Institute of Mathematics 13 Journal of Theoretical Biology 12 Nuclear Physics. B 12 Annali di Matematica Pura ed Applicata. Serie Quarta 12 Archiv der Mathematik ...and 528 more Serials all top 5 Cited in 62 Fields 2,394 Algebraic geometry (14-XX) 1,797 Commutative algebra (13-XX) 1,441 Combinatorics (05-XX) 1,197 Convex and discrete geometry (52-XX) 740 Computer science (68-XX) 587 Linear and multilinear algebra; matrix theory (15-XX) 494 Operations research, mathematical programming (90-XX) 443 Statistics (62-XX) 438 Numerical analysis (65-XX) 316 Group theory and generalizations (20-XX) 290 Biology and other natural sciences (92-XX) 281 Associative rings and algebras (16-XX) 246 Number theory (11-XX) 213 Several complex variables and analytic spaces (32-XX) 190 Field theory and polynomials (12-XX) 189 Quantum theory (81-XX) 186 Probability theory and stochastic processes (60-XX) 173 Order, lattices, ordered algebraic structures (06-XX) 157 Dynamical systems and ergodic theory (37-XX) 152 Geometry (51-XX) 124 Manifolds and cell complexes (57-XX) 123 Special functions (33-XX) 120 Algebraic topology (55-XX) 114 Ordinary differential equations (34-XX) 106 Differential geometry (53-XX) 101 Nonassociative rings and algebras (17-XX) 97 Information and communication theory, circuits (94-XX) 85 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 68 Systems theory; control (93-XX) 67 Partial differential equations (35-XX) 58 Operator theory (47-XX) 55 Real functions (26-XX) 50 Functions of a complex variable (30-XX) 46 Statistical mechanics, structure of matter (82-XX) 43 Topological groups, Lie groups (22-XX) 42 Mechanics of particles and systems (70-XX) 40 Category theory; homological algebra (18-XX) 38 General and overarching topics; collections (00-XX) 37 Mathematical logic and foundations (03-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 34 Global analysis, analysis on manifolds (58-XX) 32 Approximations and expansions (41-XX) 28 General topology (54-XX) 27 Classical thermodynamics, heat transfer (80-XX) 26 Harmonic analysis on Euclidean spaces (42-XX) 25 Functional analysis (46-XX) 21 Relativity and gravitational theory (83-XX) 19 \(K\)-theory (19-XX) 19 Difference and functional equations (39-XX) 18 General algebraic systems (08-XX) 18 Integral transforms, operational calculus (44-XX) 17 Mechanics of deformable solids (74-XX) 15 History and biography (01-XX) 8 Fluid mechanics (76-XX) 5 Potential theory (31-XX) 5 Integral equations (45-XX) 4 Abstract harmonic analysis (43-XX) 3 Mathematics education (97-XX) 2 Measure and integration (28-XX) 2 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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