Research group in Nonlinear Algebra

Head:
Bernd Sturmfels

Contact: Email
Phone:
+49 (0) 341 - 9959 - 750

Address:
Inselstr. 22
04103 Leipzig

Administrative Assistant:
Saskia Gutzschebauch
Email, Phone/Fax:
+49 (0) 341 - 9959
- 752
- 59752

Publications Bernd Sturmfels

Journal Articles

Améndola, Carlos ; Ranestad, Kristian and Bernd Sturmfels: Algebraic identifiability of Gaussian mixtures
In: International mathematics research notices, 2018 (2018) 21, p. 6556-6580
Bibtex MIS-Preprint: 76/2016 DOI: 10.1093/imrn/rnx090 ARXIV: https://arxiv.org/abs/1612.01129

Boege, Tobias ; D'Ali, Alessio ; Kahle, Thomas and Bernd Sturmfels: The geometry of Gaussoids
In: Foundations of computational mathematics, Vol. not yet known, pp. not yet known
Bibtex MIS-Preprint: 70/2017 DOI: 10.1007/s10208-018-9396-x ARXIV: https://arxiv.org/abs/1710.07175

Breiding, Paul ; Kališnik Verovšek, Sara ; Sturmfels, Bernd and Madeleine Weinstein: Learning algebraic varieties from samples
In: Revista matematica complutense, 31 (2018) 3, p. 545-593
Bibtex MIS-Preprint: 23/2018 DOI: 10.1007/s13163-018-0273-6 ARXIV: https://arxiv.org/abs/1802.09436

Helmer, Martin and Bernd Sturmfels: Nearest points on toric varieties
In: Mathematica Scandinavica, 122 (2018) 2, p. 213-238
Bibtex DOI: 10.7146/math.scand.a-101478 ARXIV: http://arxiv.org/abs/1603.06544

Kileel, Joe ; Kukelova, Zuzana ; Pajdla, Tomas and Bernd Sturmfels: Distortion varieties
In: Foundations of computational mathematics, 18 (2018) 4, p. 1043-1071
Bibtex DOI: 10.1007/s10208-017-9361-0 ARXIV: https://arxiv.org/abs/1610.01860

Kohn, Kathlén ; Sturmfels, Bernd and Matthew Trager: Changing views on curves and surfaces
In: Acta mathematica Vietnamica, 43 (2018) 1, p. 1-29
Bibtex MIS-Preprint: 39/2017 DOI: 10.1007/s40306-017-0240-1 ARXIV: https://arxiv.org/abs/1707.01877

Agarwal, Sameer ; Lee, Hon-Leung ; Sturmfels, Bernd and Rekha R. Thomas: On the existence of epipolar matrices
In: International journal of computer vision, 121 (2017) 3, p. 403-415
Bibtex DOI: 10.1007/s11263-016-0949-7 ARXIV: http://arxiv.org/abs/1510.01401

Drton, Mathias ; Kahle, Thomas ; Sturmfels, Bernd and Caroline Uhler: Algebraic statistics : 16 April - 22 April 2017 ; report no. 20/2017
In: Oberwolfach reports, 14 (2017) 2, p. 1207-1279
Bibtex DOI: 10.4171/OWR/2017/20

Kaihnsa, Nidhi ; Kummer, Mario ; Plaumann, Daniel ; Sayyary Namin, Mahsa and Bernd Sturmfels: Sixty-four curves of degree six
In: Experimental mathematics, Vol. not yet known, pp. not yet known
Bibtex MIS-Preprint: 23/2017 DOI: 10.1080/10586458.2017.1360808 ARXIV: https://arxiv.org/abs/1703.01660

Lin, Bo ; Sturmfels, Bernd ; Tang, Xiaoxian and Ruriko Yoshida: Convexity in tree spaces
In: SIAM journal on discrete mathematics, 31 (2017) 3, p. 2015-2038
Bibtex DOI: 10.1137/16M1079841 ARXIV: http://arxiv.org/abs/1510.08797

Michałek, Mateusz ; Moon, Hyunsuk ; Sturmfels, Bernd and Emanuele Ventura: Real rank geometry of ternary forms
In: Annali di matematica pura ed applicata, 196 (2017) 3, p. 1025-1054
Bibtex DOI: 10.1007/s10231-016-0606-3 ARXIV: http://arxiv.org/abs/1601.06574

Ponce, Jean ; Sturmfels, Bernd and Matthew Trager: Congruences and concurrent lines in multi-view geometry
In: Advances in applied mathematics, 88 (2017), p. 62-91
Bibtex DOI: 10.1016/j.aam.2017.01.001 ARXIV: http://de.arxiv.org/abs/1608.05924

Seigal, Anna ; Mira, Portia M. ; Sturmfels, Bernd and Miriam Barlow: Does antibiotic resistance evolve in hospitals?
In: Bulletin of mathematical biology, 79 (2017) 1, p. 191-208
Bibtex DOI: 10.1007/s11538-016-0232-7 ARXIV: http://arxiv.org/abs/1605.03660

Seigal, Anna and Bernd Sturmfels: Real rank two geometry
In: Journal of algebra, 484 (2017), p. 310-333
Bibtex DOI: 10.1016/j.jalgebra.2017.04.014 ARXIV: https://arxiv.org/abs/1609.09245

Sturmfels, Bernd: The Hurwitz form of a projective variety
In: Journal of symbolic computation, 79 (2017) 1, p. 186-196
Bibtex DOI: 10.1016/j.jsc.2016.08.012 ARXIV: http://arxiv.org/abs/1410.6703

Sturmfels, Bernd: Message from the editor-in-chief
In: SIAM journal on applied algebra and geometry, 1 (2017) 1, p. 1-1
Bibtex DOI: 10.1137/17N974240

Améndola, Carlos ; Faugère, Jean-Charles and Bernd Sturmfels: Moment varieties of Gaussian mixtures
In: Journal of algebraic statistics, 7 (2016) 1, p. 14-28
Bibtex DOI: 10.18409/jas.v7i1.42 ARXIV: http://arxiv.org/abs/1510.04654

Draisma, Jan ; Horobet, Emil ; Ottaviani, Giorgio ; Sturmfels, Bernd and Rekha R. Thomas: The Euclidean distance degree of an algebraic variety
In: Foundations of computational mathematics, 16 (2016) 1, p. 99-149
Bibtex DOI: 10.1007/s10208-014-9240-x ARXIV: http://arxiv.org/abs/1309.0049

Gross, Elizabeth ; Harrington, Heather A. ; Rosen, Zvi and Bernd Sturmfels: Algebraic systems biology : a case study for the Wnt pathway
In: Bulletin of mathematical biology, 78 (2016) 1, p. 21-51
Bibtex DOI: 10.1007/s11538-015-0125-1 ARXIV: http://arxiv.org/abs/1502.03188

Joswig, Michael ; Kileel, Joe ; Sturmfels, Bernd and André Wagner: Rigid multiview varieties
In: International journal of algebra and computation, 26 (2016) 4, p. 775-788
Bibtex DOI: 10.1142/S021819671650034X ARXIV: http://arxiv.org/abs/1509.03257

Lee, Hwangrae and Bernd Sturmfels: Duality of multiple root loci
In: Journal of algebra, 446 (2016), p. 499-526
Bibtex DOI: 10.1016/j.jalgebra.2015.08.029 ARXIV: http://arxiv.org/abs/1508.00202

Michałek, Mateusz ; Sturmfels, Bernd ; Uhler, Caroline and Piotr Zwiernik: Exponential varieties
In: Proceedings of the London Mathematical Society, 112 (2016) 1, p. 27-56
Bibtex DOI: 10.1112/plms/pdv066 ARXIV: http://arxiv.org/abs/1412.6185

Oeding, Luke ; Robeva, Elina and Bernd Sturmfels: Decomposing tensors into frames
In: Advances in applied mathematics, 73 (2016), p. 125-153
Bibtex DOI: 10.1016/j.aam.2015.10.004 ARXIV: http://arxiv.org/abs/1504.08049

Ren, Qingchun ; Shaw, Kristin and Bernd Sturmfels: Tropicalization of del Pezzo surfaces
In: Advances in mathematics, 300 (2016), p. 156-189
Bibtex DOI: 10.1016/j.aim.2016.03.017 ARXIV: http://arxiv.org/abs/1402.5651

Sturmfels, Bernd: Tensors and their eigenvectors
In: Notices of the American Mathematical Society, 63 (2016) 6, p. 604-606
Bibtex DOI: 10.1090/noti1389

Sturmfels, Bernd ; Tsukerman, Emmanuel and Lauren Williams: Symmetric matrices, Catalan paths, and correlations
In: Journal of combinatorial theory / A, 144 (2016), p. 496-510
Bibtex DOI: 10.1016/j.jcta.2016.06.014 ARXIV: http://arxiv.org/abs/1511.04125

Allman, Elizabeth S. ; Rhodes, John A. ; Sturmfels, Bernd and Piotr Zwiernik: Tensors of nonnegative rank two
In: Linear algebra and its applications, 473 (2015), p. 37-53
Bibtex DOI: 10.1016/j.laa.2013.10.046 ARXIV: http://arxiv.org/abs/1305.0539

Brodsky, Sarah ; Joswig, Michael ; Morrison, Ralph and Bernd Sturmfels: Moduli of tropical plane curves
In: Research in the mathematical sciences, 2 (2015), 4
Bibtex DOI: 10.1186/s40687-014-0018-1 ARXIV: http://arxiv.org/abs/1409.4395

Kateri, Maria ; Mohammadi, Fatemeh and Bernd Sturmfels: A family of quasisymmetry models
In: Journal of algebraic statistics, 6 (2015) 1, p. 1-16
Bibtex DOI: 10.18409/jas.v6i1.33 ARXIV: http://arxiv.org/abs/1403.0547

Kubjas, Kaie ; Robeva, Elina and Bernd Sturmfels: Fixed points of the EM algorithm and nonnegative rank boundaries
In: The annals of statistics, 43 (2015) 1, p. 422-461
Bibtex DOI: 10.1214/14-AOS1282 ARXIV: http://arxiv.org/abs/1312.5634

Mira, Portia M. ; Crona, Kristina ; Greene, Devin ; Meza, Juan C. ; Sturmfels, Bernd and Miriam Barlow: Rational design of antibiotic treatment plans : a treatment strategy for managing evolution and reversing resistance
In: PLoS one, 10 (2015) 5, e0122283
Bibtex DOI: 10.1371/journal.pone.0122283 ARXIV: http://de.arxiv.org/abs/1406.1564

Mira, Portia M. ; Crona, Kristina ; Greene, Devin ; Meza, Juan C. ; Sturmfels, Bernd and Miriam Barlow: Correction: Rational design of antibiotic treatment plans : a treatment strategy for managing evolution and reversing resistance (vol 10, e0122283, 2015)
In: PLoS one, 10 (2015) 9, e0139387
Bibtex DOI: 10.1371/journal.pone.0139387

Ottem, John Christian ; Ranestad, Kristian ; Sturmfels, Bernd and Cynthia Vinzant: Quartic spectrahedra
In: Mathematical programming, 151 (2015) 2, p. 585-612
Bibtex DOI: 10.1007/s10107-014-0844-3 ARXIV: http://arxiv.org/abs/1311.3675

Ren, Qingchun ; Richter-Gebert, Jürgen and Bernd Sturmfels: Cayley-Bacharach formulas
In: The American mathematical monthly, 122 (2015) 9, p. 845-854
Bibtex DOI: 10.4169/amer.math.monthly.122.9.845 ARXIV: http://arxiv.org/abs/1405.6438

Sinn, Rainer and Bernd Sturmfels: Generic spectrahedral shadows
In: SIAM journal on optimization, 25 (2015) 2, p. 1209-1220
Bibtex DOI: 10.1137/140978478 ARXIV: http://arxiv.org/abs/1407.5219

Hauenstein, Jonathan ; Rodriguez, Jose Israel and Bernd Sturmfels: Maximum likelihood for matrices with rank constraints
In: Journal of algebraic statistics, 5 (2014) 1, p. 18-38
Bibtex DOI: 10.18409/jas.v5i1.23 ARXIV: http://arxiv.org/abs/1210.0198

Lin, Shaowei ; Uhler, Caroline ; Sturmfels, Bernd and Peter Bühlmann: Hypersurfaces and their singularities in partial correlation testing
In: Foundations of computational mathematics, 14 (2014) 5, p. 1079-1116
Bibtex DOI: 10.1007/s10208-014-9205-0 ARXIV: http://arxiv.org/abs/1209.0285

Ottaviani, Giorgio ; Spaenlehauer, Pierre-Jean and Bernd Sturmfels: Exact solutions in structured low-rank approximation
In: SIAM journal on matrix analysis and applications, 35 (2014) 4, p. 1521-1542
Bibtex DOI: 10.1137/13094520X ARXIV: http://arxiv.org/abs/1311.2376

Ren, Qingchun ; Sam, Steven V. and Bernd Sturmfels: Tropicalization of classical moduli spaces
In: Mathematics in computer science, 8 (2014) 2, p. 119-145
Bibtex DOI: 10.1007/s11786-014-0185-x ARXIV: http://arxiv.org/abs/1303.1132

Aholt, Chris ; Sturmfels, Bernd and Rekha R. Thomas: A Hilbert scheme in computer vision
In: Canadian journal of mathematics, 65 (2013) 5, p. 961-988
Bibtex DOI: 10.4153/CJM-2012-023-2 ARXIV: http://arxiv.org/abs/1107.2875

Cartwright, Dustin and Bernd Sturmfels: The number of eigenvalues of a tensor
In: Linear algebra and its applications, 438 (2013) 2, p. 942-952
Bibtex DOI: 10.1016/j.laa.2011.05.040 ARXIV: http://arxiv.org/abs/1004.4953

Cattani, Eduardo ; Cueto, Maria Angélica ; Dickenstein, Alicia ; Di Rocco, Sandra and Bernd Sturmfels: Mixed discriminants
In: Mathematische Zeitschrift, 274 (2013) 3-4, p. 761-778
Bibtex DOI: 10.1007/s00209-012-1095-8 ARXIV: http://arxiv.org/abs/1112.1012

Engström, Alexander ; Hersh, Patricia and Bernd Sturmfels: Toric cubes
In: Rendiconti del Circolo Matematico di Palermo, 62 (2013) 1, p. 67-78
Bibtex DOI: 10.1007/s12215-013-0115-9 ARXIV: http://arxiv.org/abs/1202.4333

Manjunath, Madhusudan and Bernd Sturmfels: Monomials, binomials and Riemann-Roch
In: Journal of algebraic combinatorics : an international journal, 37 (2013) 4, p. 737-756
Bibtex DOI: 10.1007/s10801-012-0386-9 ARXIV: http://arxiv.org/abs/1201.4357

Morgenshtern, Veniamin I. ; Riegler, Erwin ; Yang, Wei ; Durisi, Giuseppe ; Lin, Shaowei ; Sturmfels, Bernd and Helmut Bölcskei: Capacity pre-log of noncoherent SIMO channels via Hironaka's theorem
In: IEEE transactions on information theory, 59 (2013) 7, p. 4213-4229
Bibtex DOI: 10.1109/TIT.2013.2251394 ARXIV: http://arxiv.org/abs/1204.2775

Ottaviani, Giorgio and Bernd Sturmfels: Matrices with eigenvectors in a given subspace
In: Proceedings of the American Mathematical Society, 141 (2013) 4, p. 1219-1232
Bibtex DOI: 10.1090/S0002-9939-2012-11404-2 ARXIV: http://arxiv.org/abs/1012.1016

Ren, Qingchun ; Sam, Steven V. ; Schrader, Gus and Bernd Sturmfels: The universal Kummer threefold
In: Experimental mathematics, 22 (2013) 3, p. 327-362
Bibtex DOI: 10.1080/10586458.2013.816206 ARXIV: http://arxiv.org/abs/1208.1229

Sanyal, Raman ; Sturmfels, Bernd and Cynthia Vinzant: The entropic discriminant
In: Advances in mathematics, 244 (2013), p. 678-707
Bibtex DOI: 10.1016/j.aim.2013.05.019 ARXIV: http://arxiv.org/abs/1108.2925

Sturmfels, Bernd and Ngoc Mai Tran: Combinatorial types of tropical eigenvectors
In: The bulletin of the London Mathematical Society, 45 (2013) 1, p. 27-36
Bibtex DOI: 10.1112/blms/bds058 ARXIV: http://arxiv.org/abs/1105.5504

Sturmfels, Bernd and Piotr Zwiernik: Binary cumulant varieties
In: Annals of combinatorics, 17 (2013) 1, p. 229-250
Bibtex DOI: 10.1007/s00026-012-0174-1 ARXIV: http://arxiv.org/abs/1103.0153

Blekherman, Grigoriy ; Hauenstein, Jonathan ; Ottem, John Christian ; Ranestad, Kristian and Bernd Sturmfels: Algebraic boundaries of Hilbert's SOS cones
In: Compositio mathematica, 148 (2012) 6, p. 1717-1735
Bibtex DOI: 10.1112/S0010437X12000437 ARXIV: http://arxiv.org/abs/1107.1846

De Loera, Jesús A. ; Sturmfels, Bernd and Cynthia Vinzant: The central curve in linear programming
In: Foundations of computational mathematics, 12 (2012) 4, p. 509-540
Bibtex DOI: 10.1007/s10208-012-9127-7 ARXIV: http://arxiv.org/abs/1012.3978

Filiz, Ismail Onur ; Guo, Xin ; Morton, Jason and Bernd Sturmfels: Graphical models for correlated defaults
In: Mathematical finance : an international journal of mathematics, statistics and financial economics, 22 (2012) 4, p. 621-644
Bibtex DOI: 10.1111/j.1467-9965.2011.00499.x ARXIV: https://arxiv.org/abs/0809.1393

Ranestad, Kristian and Bernd Sturmfels: On the convex hull of a space curve
In: Advances in geometry, 12 (2012) 1, p. 157-178
Bibtex DOI: 10.1515/advgeom.2011.021 ARXIV: http://arxiv.org/abs/0912.2986

Sturmfels, Bernd: Geometry of higher-order Markov chains
In: Journal of algebraic statistics, 3 (2012) 1, p. 1-10
Bibtex DOI: 10.18409/jas.v3i1.13 ARXIV: http://arxiv.org/abs/1207.1899

Sturmfels, Bernd and Volkmar Welker: Commutative algebra of statistical ranking
In: Journal of algebra, 361 (2012), p. 264-286
Bibtex DOI: 10.1016/j.jalgebra.2012.03.028 ARXIV: http://arxiv.org/abs/1101.1597

Brodsky, Sarah B. and Bernd Sturmfels: Tropical quadrics through three points
In: Linear algebra and its applications, 435 (2011) 7, p. 1778-1785
Bibtex DOI: 10.1016/j.laa.2010.05.004 ARXIV: http://arxiv.org/abs/1002.0603

Cartwright, Dustin ; Häbich, Mathias ; Sturmfels, Bernd and Annette Werner: Mustafin varieties
In: Selecta mathematica, 17 (2011) 4, p. 757-793
Bibtex DOI: 10.1007/s00029-011-0075-x ARXIV: http://arxiv.org/abs/1002.1418

Plaumann, Daniel ; Sturmfels, Bernd and Cynthia Vinzant: Quartic curves and their bitangents
In: Journal of symbolic computation, 46 (2011) 6, p. 712-733
Bibtex DOI: 10.1016/j.jsc.2011.01.007 ARXIV: http://arxiv.org/abs/1008.4104

Sanyal, Raman ; Sottile, Frank and Bernd Sturmfels: Orbitopes
In: Mathematika : a journal of pure and applied mathematics, 57 (2011) 2, p. 275-314
Bibtex DOI: 10.1112/S002557931100132X ARXIV: http://arxiv.org/abs/0911.5436

Cartwright, Dustin and Bernd Sturmfels: The Hilbert scheme of the diagonal in a product of projective spaces
In: International mathematics research notices, 2010 (2010) 9, p. 1741-1771
Bibtex DOI: 10.1093/imrn/rnp201 ARXIV: http://arxiv.org/abs/0901.0212

Evans, Steven N. ; Sturmfels, Bernd and Caroline Uhler: Commuting birth-and-death processes
In: The annals of applied probability, 20 (2010) 1, p. 238-266
Bibtex DOI: 10.1214/09-AAP615 ARXIV: http://arxiv.org/abs/0812.2724

Nie, Jiawang ; Ranestad, Kristian and Bernd Sturmfels: The algebraic degree of semidefinite programming
In: Mathematical programming, 122 (2010) 2, p. 379-405
Bibtex DOI: 10.1007/s10107-008-0253-6 ARXIV: https://arxiv.org/abs/math/0611562

Rostalski, Philipp and Bernd Sturmfels: Dualities in convex algebraic geometry
In: Rendiconti di matematica e delle sue applicazioni, 30 (2010) 3-4, p. 285-327
Bibtex ARXIV: http://arxiv.org/abs/1006.4894 LINK: http://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2010%283-4%29/285-327.pdf

Shiu, Anne and Bernd Sturmfels: Siphons in chemical reaction networks
In: Bulletin of mathematical biology, 72 (2010) 6, p. 1448-1463
Bibtex DOI: 10.1007/s11538-010-9502-y ARXIV: http://arxiv.org/abs/0904.4529

Sturmfels, Bernd and Caroline Uhler: Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
In: Annals of the institute of statistical mathematics, 62 (2010) 4, p. 603-638
Bibtex DOI: 10.1007/s10463-010-0295-4 ARXIV: http://arxiv.org/abs/0906.3529

Sturmfels, Bernd and Mauricio Velasco: Blow-ups of \(\mathbb{P}^{n-3}\) at \(n\) points and spinor varieties
In: Journal of commutative algebra, 2 (2010) 2, p. 223-244
Bibtex DOI: 10.1216/JCA-2010-2-2-223 ARXIV: http://arxiv.org/abs/0906.5096

Sturmfels, Bernd and Zhiqiang Xu: Sagbi bases of Cox-Nagata rings
In: Journal of the European Mathematical Society, 12 (2010) 2, p. 429-459
Bibtex DOI: 10.4171/JEMS/204 ARXIV: https://arxiv.org/abs/0803.0892

Cartwright, Dustin A. ; Brady, Siobhan M. ; Orlando, David A. ; Sturmfels, Bernd and Philip N. Benfey: Reconstructing spatiotemporal gene expression data from partial observations
In: Bioinformatics, 25 (2009) 19, p. 2581-2587
Bibtex DOI: 10.1093/bioinformatics/btp437 ARXIV: http://arxiv.org/abs/0903.4027

Craciun, Gheorghe ; Dickenstein, Alicia ; Shiu, Anne and Bernd Sturmfels: Toric dynamical systems
In: Journal of symbolic computation, 44 (2009) 11, p. 1551-1565
Bibtex DOI: 10.1016/j.jsc.2008.08.006 ARXIV: http://arxiv.org/abs/0708.3431

Dueck, Pierre ; Hosten, Serkan and Bernd Sturmfels: Normal toric ideals of low codimension
In: Journal of pure and applied algebra, 213 (2009) 8, p. 1636-1641
Bibtex DOI: 10.1016/j.jpaa.2008.11.045 ARXIV: http://arxiv.org/abs/0801.3826

Gritzmann, Peter ; Sturmfels, Bernd and Günter M. Ziegler: Guest editors' foreword : [special issue dedicated to the memory of Victor Klee]
In: Discrete and computational geometry, 42 (2009) 2, p. 131-131
Bibtex DOI: 10.1007/s00454-009-9191-1

Herrmann, Sven ; Jensen, Anders ; Joswig, Michael and Bernd Sturmfels: How to draw tropical planes
In: The electronic journal of combinatorics, 16 (2009) 2, R6
Bibtex ARXIV: http://arxiv.org/abs/0808.2383 LINK: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i2r6

Laubenbacher, Reinhard and Bernd Sturmfels: Computer algebra in systems biology
In: The American mathematical monthly, 116 (2009) 10, p. 882-891
Bibtex DOI: 10.4169/000298909X477005 ARXIV: http://arxiv.org/abs/0712.4248

Laubenbacher, Reinhard and Bernd Sturmfels: Computeralgebra in der Systembiologie
In: Informatik-Spektrum, 32 (2009) 1, p. 27-32
Bibtex DOI: 10.1007/s00287-008-0307-4

Lin, Shaowei and Bernd Sturmfels: Polynomial relations among principal minors of a 4 x 4-matrix
In: Journal of algebra, 322 (2009) 11, p. 4121-4131
Bibtex DOI: 10.1016/j.jalgebra.2009.06.026 ARXIV: http://arxiv.org/abs/0812.0601

Lin, Shaowei ; Sturmfels, Bernd and Zhiqiang Xu: Marginal likelihood integrals for mixtures of independence models
In: Journal of machine learning research, 10 (2009), p. 1611-1631
Bibtex ARXIV: http://arxiv.org/abs/0805.3602 LINK: http://www.jmlr.org/papers/volume10/lin09a/lin09a.pdf

Morton, Jason ; Pachter, Lior ; Shiu, Anne ; Sturmfels, Bernd and Oliver Wienand: Convex rank tests and semigraphoids
In: SIAM journal on discrete mathematics, 23 (2009) 3, p. 1117-1134
Bibtex DOI: 10.1137/080715822 ARXIV: http://arxiv.org/abs/math/0702564

Nie, Jiawang and Bernd Sturmfels: Matrix cubes parameterized by eigenvalues
In: SIAM journal on matrix analysis and applications, 31 (2009) 2, p. 755-766
Bibtex DOI: 10.1137/080722606 ARXIV: http://arxiv.org/abs/0804.4462

Speyer, David and Bernd Sturmfels: Tropical mathematics
In: Mathematics magazine, 82 (2009) 3, p. 163-173
Bibtex ARXIV: http://arxiv.org/abs/math/0408099 LINK: http://www.jstor.org/stable/27765897

Bogart, Tristram ; Jensen, Anders ; Speyer, David ; Sturmfels, Bernd and Rekha R. Thomas: Computing tropical varieties
In: Topologica, 1 (2008) 1, P 007
Bibtex DOI: 10.3731/topologica.1.007 ARXIV: http://arxiv.org/abs/math/0507563

Dequéant, Mary-Lee ; Ahnert, Sebastian ; Edelsbrunner, Herbert ; Fink, Thomas M. A. ; Glynn, Earl F. ; Hattem, Gaye ; Kudlicki, Andrzej ; Mileyko, Yuriy ; Morton, Jason ; Mushegian, Arcady R. ; Pachter, Lior ; Rowicka, Maga ; Shiu, Anne ; Sturmfels, Bernd and Olivier Pourquié: Comparison of pattern detection methods in microarray time series of the segmentation clock
In: PLoS one, 3 (2008) 8, e2856
Bibtex DOI: 10.1371/journal.pone.0002856

Gritzmann, Peter and Bernd Sturmfels: Victor L. Klee 1925-2007
In: Notices of the American Mathematical Society, 55 (2008) 4, p. 467-473
Bibtex LINK: http://www.ams.org/notices/200804/tx080400467p.pdf

Hemmecke, Raymond ; Morton, Jason ; Shiu, Anne ; Sturmfels, Bernd and Oliver Wienand: Three counter-examples on semi-graphoids
In: Combinatorics, probability and computing, 17 (2008) 02, p. 239-257
Bibtex DOI: 10.1017/S0963548307008838 ARXIV: https://arxiv.org/abs/math/0610451

Huggins, Peter ; Sturmfels, Bernd ; Yu, Josephine and Debbie S. Yuster: The hyperdeterminant and triangulations of the 4-cube
In: Mathematics of computation, 77 (2008) 263, p. 1653-1679
Bibtex ARXIV: https://arxiv.org/abs/math/0602149 LINK: http://www.jstor.org/stable/40234576

Sturmfels, Bernd and Seth Sullivant: Toric geometry of cuts and splits
In: The Michigan mathematical journal, 57 (2008), p. 689-709
Bibtex DOI: 10.1307/mmj/1220879432 ARXIV: https://arxiv.org/abs/math/0606683

Sturmfels, Bernd and Jenia Tevelev: Elimination theory for tropical varieties
In: Mathematical research letters, 15 (2008) 3, p. 543-562
Bibtex DOI: 10.4310/MRL.2008.v15.n3.a14 ARXIV: http://arxiv.org/abs/0704.3471

Beerenwinkel, Niko ; Eriksson, Nicholas and Bernd Sturmfels: Conjunctive Bayesian networks
In: Bernoulli, 13 (2007) 4, p. 893-909
Bibtex DOI: 10.3150/07-BEJ6133 ARXIV: http://arxiv.org/abs/math/0608417

Beerenwinkel, Niko ; Pachter, Lior and Bernd Sturmfels: Epistasis and shapes of fitness landscapes
In: Statistica Sinica, 17 (2007) 4, p. 1317-1342
Bibtex ARXIV: http://arxiv.org/abs/q-bio/0603034 LINK: http://www.jstor.org/stable/24307677

Beerenwinkel, Niko ; Pachter, Lior ; Sturmfels, Bernd ; Elena, Santiago F. and Richard E. Lenski: Analysis of epistatic interactions and fitness landscapes using a new geometric approach
In: BMC evolutionary biology, 7 (2007), 60
Bibtex DOI: 10.1186/1471-2148-7-60

Bogart, Tristram ; Jensen, Anders ; Speyer, David ; Sturmfels, Bernd and Rekha R. Thomas: Computing tropical varieties
In: Journal of symbolic computation, 42 (2007) 1-2, p. 54-73
Bibtex DOI: 10.1016/j.jsc.2006.02.004 ARXIV: http://arxiv.org/abs/math/0507563

Dickenstein, Alicia ; Feichtner, Eva Maria and Bernd Sturmfels: Tropical discriminants
In: Journal of the American Mathematical Society, 20 (2007) 4, p. 1111-1133
Bibtex DOI: 10.1090/S0894-0347-07-00562-0 ARXIV: http://arxiv.org/abs/math/0510126

Drton, Mathias ; Sturmfels, Bernd and Seth Sullivant: Algebraic factor analysis : tetrads, pentads and beyond
In: Probability theory and related fields, 138 (2007) 3-4, p. 463-493
Bibtex DOI: 10.1007/s00440-006-0033-2 ARXIV: http://arxiv.org/abs/math/0509390

Holtz, Olga and Bernd Sturmfels: Hyperdeterminantal relations among symmetric principal minors
In: Journal of algebra, 316 (2007) 2, p. 634-648
Bibtex DOI: 10.1016/j.jalgebra.2007.01.039 ARXIV: http://arxiv.org/abs/math/0604374

Hosten, Serkan and Bernd Sturmfels: Computing the integer programming gap
In: Combinatorica, 27 (2007) 3, p. 367-382
Bibtex DOI: 10.1007/s00493-007-2057-3 ARXIV: http://arxiv.org/abs/math/0301266

Huggins, Peter ; Pachter, Lior and Bernd Sturmfels: Toward the human genotope
In: Bulletin of mathematical biology, 69 (2007) 8, p. 2723-2735
Bibtex DOI: 10.1007/s11538-007-9244-7 ARXIV: http://arxiv.org/abs/q-bio/0611032

Joswig, Michael ; Sturmfels, Bernd and Josephine Yu: Affine buildings and tropical convexity
In: Albanian journal of mathematics, 1 (2007) 4, p. 187-211
Bibtex ARXIV: http://arxiv.org/abs/0706.1918

Morton, Jason ; Pachter, Lior ; Shiu, Anne and Bernd Sturmfels: The cyclohedron test for finding periodic genes in time course expression studies
In: Statistical applications in genetics and molecular biology, 6 (2007) 1, 21
Bibtex DOI: 10.2202/1544-6115.1286 ARXIV: http://arxiv.org/abs/q-bio/0702049

Pachter, Lior and Bernd Sturmfels: The mathematics of phylogenomics
In: SIAM review, 49 (2007) 1, p. 3-31
Bibtex DOI: 10.1137/050632634 ARXIV: http://arxiv.org/abs/math/0409132

Sturmfels, Bernd ; Tevelev, Jenia and Josephine Yu: The Newton polytope of the implicit equation

Beerenwinkel, Niko ; Eriksson, Nicholas and Bernd Sturmfels: Evolution on distributive lattices
In: Journal of theoretical biology, 242 (2006) 2, p. 409-420
Bibtex DOI: 10.1016/j.jtbi.2006.03.013 ARXIV: http://arxiv.org/abs/q-bio/0511039

Catanese, Fabrizio ; Hosten, Serkan ; Khetan, Amit and Bernd Sturmfels: The maximum likelihood degree
In: American journal of mathematics, 128 (2006) 3, p. 671-697
Bibtex DOI: 10.1353/ajm.2006.0019 ARXIV: http://arxiv.org/abs/math/0406533

Colón-Reyes, Omar ; Jarrah, Abdul Salam ; Laubenbacher, Reinhard and Bernd Sturmfels: Monomial dynamical systems over finite fields

Dewey, Colin N. ; Huggins, Peter M. ; Woods, Kevin ; Sturmfels, Bernd and Lior Pachter: Parametric alignment of Drosophila genomes
In: PLoS computational biology, 2 (2006) 6, p. 606-614
Bibtex DOI: 10.1371/journal.pcbi.0020073 ARXIV: http://arxiv.org/abs/q-bio/0512008

Geiger, Dan ; Meek, Christopher and Bernd Sturmfels: On the toric algebra of graphical models
In: The annals of statistics, 34 (2006) 3, p. 1463-1492
Bibtex DOI: 10.1214/009053606000000263 ARXIV: https://arxiv.org/abs/math/0608054

Hallgrimsdóttir, Ingileif B. and Bernd Sturmfels: Resultants in genetic linkage analysis
In: Journal of symbolic computation, 41 (2006) 2, p. 125-137
Bibtex DOI: 10.1016/j.jsc.2005.04.012 ARXIV: http://arxiv.org/abs/q-bio/0405001

Nie, Jiawang ; Demmel, James and Bernd Sturmfels: Minimizing polynomials via sum of squares over the gradient ideal
In: Mathematical programming, 106 (2006) 3, p. 587-606
Bibtex DOI: 10.1007/s10107-005-0672-6 ARXIV: http://arxiv.org/abs/math/0411342

Sturmfels, Bernd and Seth Sullivant: Combinatorial secant varieties
In: Pure and applied mathematics quarterly, 2 (2006) 3, p. 867-891
Bibtex DOI: 10.4310/PAMQ.2006.v2.n3.a12 ARXIV: http://arxiv.org/abs/math/0506223

Altmann, Klaus and Bernd Sturmfels: The graph of monomial ideals
In: Journal of pure and applied algebra, 201 (2005) 1-3, p. 250-263
Bibtex DOI: 10.1016/j.jpaa.2004.12.030 ARXIV: http://arxiv.org/abs/math/0209152

Feichtner, Eva Maria and Bernd Sturmfels: Matroid polytopes, nested sets and Bergman fans
In: Portugaliae mathematica, 62 (2005) 4, p. 437-468
Bibtex ARXIV: http://arxiv.org/abs/math/0411260 LINK: http://www.emis.ams.org/journals/PM/62f4/3.html

Garcia, Luis David ; Stillman, Michael E. and Bernd Sturmfels: Algebraic geometry of Bayesian networks
In: Journal of symbolic computation, 39 (2005) 3-4, p. 331-355
Bibtex DOI: 10.1016/j.jsc.2004.11.007 ARXIV: http://arxiv.org/abs/math/0301255

Hosten, Serkan ; Khetan, Amit and Bernd Sturmfels: Solving the likelihood equations
In: Foundations of computational mathematics, 5 (2005) 4, p. 389-407
Bibtex DOI: 10.1007/s10208-004-0156-8 ARXIV: http://arxiv.org/abs/math/0408270

Sturmfels, Bernd: What is a Gröbner basis?
In: Notices of the American Mathematical Society, 52 (2005) 10, p. 1199-1200
Bibtex LINK: http://www.ams.org/publications/notices/whatis/noticesarchive

Sturmfels, Bernd: Can biology lead to new theorems?
In: Annual report of the Clay Mathematics Institute, 2005 (2005), p. 13-26
Bibtex LINK: http://groups.claymath.org/library/annual_report/ar2005/05report_featurearticle.pdf

Sturmfels, Bernd and Seth Sullivant: Toric ideals of phylogenetic invariants
In: Journal of computational biology, 12 (2005) 2, p. 204-228
Bibtex DOI: 10.1089/cmb.2005.12.204 ARXIV: http://arxiv.org/abs/q-bio/0402015

De Loera, Jesús A. ; Haws, David ; Hemmecke, Raymond ; Huggins, Peter ; Sturmfels, Bernd and Ruriko Yoshida: Short rational functions for toric algebra and applications
In: Journal of symbolic computation, 38 (2004) 2, p. 959-973
Bibtex DOI: 10.1016/j.jsc.2004.02.001 ARXIV: https://arxiv.org/abs/math/0307350

Develin, Mike and Bernd Sturmfels: Tropical convexity

Develin, Mike and Bernd Sturmfels: Erratum for 'Tropical convexity' [Doc. Math. 9 (2004), 1-27]
In: Documenta mathematica, 9 (2004), p. 205-206
Bibtex LINK: http://www.emis.ams.org/journals/DMJDMV/vol-09/12.html

Haiman, Mark and Bernd Sturmfels: Multigraded Hilbert schemes
In: Journal of algebraic geometry, 13 (2004) 4, p. 725-769
Bibtex DOI: 10.1090/S1056-3911-04-00373-X ARXIV: http://arxiv.org/abs/math/0201271

Hosten, Serkan ; Maclagan, Diane and Bernd Sturmfels: Supernormal vector configurations
In: Journal of algebraic combinatorics : an international journal, 19 (2004) 3, p. 297-313
Bibtex DOI: 10.1023/B:JACO.0000030705.93448.ce ARXIV: https://arxiv.org/abs/math/0105036

Pachter, Lior and Bernd Sturmfels: Parametric inference for biological sequence analysis
In: Proceedings of the National Academy of Sciences of the United States of America, 101 (2004) 46, p. 16138-16143
Bibtex DOI: 10.1073/pnas.0406011101 ARXIV: http://arxiv.org/abs/q-bio/0401033

Pachter, Lior and Bernd Sturmfels: Tropical geometry of statistical models
In: Proceedings of the National Academy of Sciences of the United States of America, 101 (2004) 46, p. 16132-16137
Bibtex DOI: 10.1073/pnas.0406010101 ARXIV: https://arxiv.org/abs/q-bio/0311009

Speyer, David and Bernd Sturmfels: The tropical Grassmannian
In: Advances in geometry, 4 (2004) 3, p. 389-411
Bibtex DOI: 10.1515/advg.2004.023 ARXIV: http://arxiv.org/abs/math/0304218

Sturmfels, Bernd and Josephine Yu: Classification of six-point metrics
In: The electronic journal of combinatorics, 11 (2004) 1, R44
Bibtex ARXIV: http://arxiv.org/abs/math/0403147 LINK: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v11i1r44

De Loera, Jesús A. and Bernd Sturmfels: Algebraic unimodular counting
In: Mathematical programming, 96 (2003) 2, p. 183-203
Bibtex DOI: 10.1007/s10107-003-0383-9 ARXIV: http://arxiv.org/abs/math/0104286

Santos, Francisco and Bernd Sturmfels: Higher Lawrence configurations
In: Journal of combinatorial theory / A, 103 (2003) 1, p. 151-164
Bibtex DOI: 10.1016/S0097-3165(03)00092-X ARXIV: https://arxiv.org/abs/math/0209326

Santos, Francisco and Bernd Sturmfels: Alexander duality in subdivisions of Lawrence polytopes
In: Advances in geometry, 3 (2003) 2, p. 177-189
Bibtex DOI: 10.1515/advg.2003.012 ARXIV: https://arxiv.org/abs/math/0202104

Cattani, Eduardo ; Dickenstein, Alicia and Bernd Sturmfels: Binomial residues
In: Annales de l'Institut Fourier, 52 (2002) 3, p. 687-708
Bibtex DOI: 10.5802/aif.1898 ARXIV: http://arxiv.org/abs/math/0003178

De Loera, Jesús A. ; Sottile, Frank and Bernd Sturmfels: Guest editors' foreword : [papers from the special session on algebraic and geometric combinatorics at the AMS Western Section Meeting, San Francisco, CA, USA, October 21-22 and the Bay Area Discrete Math Day, University of California, Davis, CA, USA, October 20, 2000]
In: Discrete and computational geometry, 27 (2002) 1, p. 1-2
Bibtex DOI: 10.1007/s00454-001-0048-5

Dickenstein, Alicia and Bernd Sturmfels: Elimination theory in codimension 2
In: Journal of symbolic computation, 34 (2002) 2, p. 119-135
Bibtex DOI: 10.1006/jsco.2002.0545 ARXIV: https://arxiv.org/abs/math/0102204

Hausel, Tamás and Bernd Sturmfels: Toric hyperkähler varieties

Novik, Isabella ; Postnikov, Alexander and Bernd Sturmfels: Syzygies of oriented matroids
In: Duke mathematical journal, 111 (2002) 2, p. 287-317
Bibtex DOI: 10.1215/S0012-7094-02-11124-7 ARXIV: https://arxiv.org/abs/math/0009241

Bayer, Dave ; Popescu, Sorin and Bernd Sturmfels: Syzygies of unimodular Lawrence ideals
In: Journal für die reine und angewandte Mathematik, 2001 (2001) 534, p. 169-186
Bibtex DOI: 10.1515/crll.2001.040 ARXIV: https://arxiv.org/abs/math/9912247

Cattani, Eduardo ; Dickenstein, Alicia and Bernd Sturmfels: Rational hypergeometric functions
In: Compositio mathematica, 128 (2001) 2, p. 217-240
Bibtex DOI: 10.1023/A:1017541231618 ARXIV: http://arxiv.org/abs/math/9911030

Sottile, Frank and Bernd Sturmfels: A sagbi basis for the quantum Grassmannian
In: Journal of pure and applied algebra, 158 (2001) 2-3, p. 347-366
Bibtex DOI: 10.1016/S0022-4049(00)00053-0 ARXIV: https://arxiv.org/abs/math/9908016

Miller, Ezra ; Sturmfels, Bernd and Kohji Yanagawa: Generic and cogeneric monomial ideals
In: Journal of symbolic computation, 29 (2000) 4-5, p. 691-708
Bibtex DOI: 10.1006/jsco.1999.0290 ARXIV: http://arxiv.org/abs/math/9812126

Sturmfels, Bernd: Four counterexamples in combinatorial algebraic geometry
In: Journal of algebra, 230 (2000) 1, p. 282-294
Bibtex DOI: 10.1006/jabr.1999.7950

Sturmfels, Bernd: Solving algebraic equations in terms of A-hypergeometric series
In: Discrete mathematics, 210 (2000) 1-3, p. 171-181
Bibtex DOI: 10.1016/S0012-365X(99)00126-0

Onn, Shmuel and Bernd Sturmfels: Cutting corners
In: Advances in applied mathematics, 23 (1999) 1, p. 29-48
Bibtex DOI: 10.1006/aama.1999.0645

Saito, Mutsumi ; Sturmfels, Bernd and Nobuki Takayama: Hypergeometric polynomials and integer programming
In: Compositio mathematica, 115 (1999) 2, p. 231-240
Bibtex DOI: 10.1023/A:1000609524994

Sturmfels, Bernd ; Cattani, Eduardo and Alicia Dickenstein: The search for rational A-hypergeometric functions
In: ACM SIGSAM bulletin, 33 (1999) 3, p. 15-15
Bibtex DOI: 10.1145/347127.347197

Bayer, Dave ; Peeva, Irena and Bernd Sturmfels: Monomial resolutions
In: Mathematical research letters, 5 (1998) 1-2, p. 31-46
Bibtex DOI: 10.4310/MRL.1998.v5.n1.a3 ARXIV: https://arxiv.org/abs/alg-geom/9610012

Bayer, Dave and Bernd Sturmfels: Cellular resolutions of monomial modules
In: Journal für die reine und angewandte Mathematik, 502 (1998), p. 123-140
Bibtex DOI: 10.1515/crll.1998.083 ARXIV: http://arxiv.org/abs/alg-geom/9711023

Cattani, Eduardo ; Dickenstein, Alicia and Bernd Sturmfels: Residues and resultants
In: Journal of mathematical sciences, 5 (1998) 1, p. 119-148
Bibtex ARXIV: https://arxiv.org/abs/alg-geom/9702001 LINK: http://www.ms.u-tokyo.ac.jp/journal/abstract/jms050106.html

Diaconis, Persi and Bernd Sturmfels: Algebraic algorithms for sampling from conditional distributions
In: The annals of statistics, 26 (1998) 1, p. 363-397
Bibtex LINK: http://www.jstor.org/stable/119991

Eisenbud, David ; Peeva, Irena and Bernd Sturmfels: Non-commutative Gröbner bases for commutative algebras
In: Proceedings of the American Mathematical Society, 126 (1998) 3, p. 687-691
Bibtex DOI: 10.1090/S0002-9939-98-04229-4

Huber, Birkett ; Sottile, Frank and Bernd Sturmfels: Numerical Schubert calculus
In: Journal of symbolic computation, 26 (1998) 6, p. 767-788
Bibtex DOI: 10.1006/jsco.1998.0239 ARXIV: https://arxiv.org/abs/alg-geom/9706004

Peeva, Irena ; Reiner, Victor and Bernd Sturmfels: How to shell a monoid
In: Mathematische Annalen, 310 (1998) 2, p. 379-393
Bibtex DOI: 10.1007/s002080050152

Peeva, Irena and Bernd Sturmfels: Syzygies of codimension 2 lattice ideals
In: Mathematische Zeitschrift, 229 (1998) 1, p. 163-194
Bibtex DOI: 10.1007/PL00004645

Peeva, Irena and Bernd Sturmfels: Generic lattice ideals
In: Journal of the American Mathematical Society, 11 (1998) 2, p. 363-373
Bibtex LINK: http://www.jstor.org/stable/2646153

Roos, Jan-Erik and Bernd Sturmfels: A toric ring with irrational Poincare-Betti series
In: Comptes rendus de l'Académie des Sciences / 1, 326 (1998) 2, p. 141-146
Bibtex DOI: 10.1016/S0764-4442(97)89459-1

Saito, Mutsumi ; Sturmfels, Bernd and Nobuki Takayama: Gröbner deformations of regular holonomic systems
In: Proceedings of the Japan Academy : series A, mathematical sciences, 74 (1998) 7, p. 111-113
Bibtex DOI: 10.3792/pjaa.74.111

Sturmfels, Bernd: Polynomial equations and convex polytopes
In: The American mathematical monthly, 105 (1998) 10, p. 907-922
Bibtex DOI: 10.2307/2589283

Fulton, William and Bernd Sturmfels: Intersection theory on toric varieties
In: Topology, 36 (1997) 2, p. 335-353
Bibtex DOI: 10.1016/0040-9383(96)00016-X ARXIV: http://de.arxiv.org/abs/alg-geom/9403002

Guckenheimer, John ; Myers, Mark and Bernd Sturmfels: Computing Hopf bifurcations 1.
In: SIAM journal on numerical analysis, 34 (1997) 1, p. 1-21
Bibtex DOI: 10.1137/S0036142993253461

Huber, Birkett and Bernd Sturmfels: Bernstein's theorem in affine space
In: Discrete and computational geometry, 17 (1997) 2, p. 137-141
Bibtex DOI: 10.1007/BF02770870

Saito, Mutsumi ; Sturmfels, Bernd and Nobuki Takayama: Hypergeometric polynomials and integer programming [Japanese]
In: Surikaisekikenkyusho Kokyuroku = RIMS Kokyuroku, 986 (1997), p. 31-33
Bibtex LINK: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/0986-5.pdf

Sturmfels, Bernd and Markus Wiegelmann: Structural Gröbner basis detection
In: Applicable algebra in engineering, communication and computing, 8 (1997) 4, p. 257-263
Bibtex DOI: 10.1007/s002000050063

Thomas, Rekha R. and Bernd Sturmfels: Variation of cost functions in integer programming
In: Mathematical programming, 77 (1997) 2, p. 357-387
Bibtex DOI: 10.1007/BF02614622

De Loera, Jesús A. ; Hosten, Serkan ; Santos, Francisco and Bernd Sturmfels: The polytope of all triangulations of a point configuration
In: Documenta mathematica, 1 (1996), p. 103-119
Bibtex LINK: http://www.emis.ams.org/journals/DMJDMV/vol-01/04.html

Eisenbud, David and Bernd Sturmfels: Binomial ideals
In: Duke mathematical journal, 84 (1996) 1, p. 1-45
Bibtex DOI: 10.1215/S0012-7094-96-08401-X ARXIV: https://arxiv.org/abs/alg-geom/9401001

Laubenbacher, Reinhard and Bernd Sturmfels: A normal form algorithm for modules over k[x,y]/(xy)
In: Journal of algebra, 184 (1996) 3, p. 1001-1024
Bibtex DOI: 10.1006/jabr.1996.0295

De Loera, Jesús A. ; Sturmfels, Bernd and Rekha R. Thomas: Gröbner bases and triangulations of the second hypersimplex
In: Combinatorica, 15 (1995) 3, p. 409-424
Bibtex DOI: 10.1007/BF01299745

Fulton, William ; MacPherson, Robert D. ; Sottile, Frank and Bernd Sturmfels: Intersection theory on spherical varieties
In: Journal of algebraic geometry, 4 (1995) 1, p. 181-193
Bibtex

Huber, Birkett and Bernd Sturmfels: A polyhedral method for solving sparse polynomial systems
In: Mathematics of computation, 64 (1995) 212, p. 1541-1555
Bibtex DOI: 10.2307/2153370

Kalkbrener, Michael and Bernd Sturmfels: Initial complexes of prime ideals
In: Advances in mathematics, 116 (1995) 2, p. 365-376
Bibtex DOI: 10.1006/aima.1995.1071

Sturmfels, Bernd: On vector partition functions
In: Journal of combinatorial theory / A, 72 (1995) 2, p. 302-309
Bibtex DOI: 10.1016/0097-3165(95)90067-5

Sturmfels, Bernd ; Trung, Ngo Viet and Wolfgang Vogel: Bounds on degrees of projective schemes
In: Mathematische Annalen, 302 (1995) 1, p. 417-432
Bibtex DOI: 10.1007/BF01444501

Sturmfels, Bernd ; Weismantel, Robert and Günter M. Ziegler: Gröbner bases of lattices, corner polyhedra, and integer programming
In: Beiträge zur Algebra und Geometrie, 36 (1995) 2, p. 281-298
Bibtex LINK: http://www.emis.de/journals/BAG/vol.36/no.2/

Billera, Louis J. ; Kapranov, Mikhail M. and Bernd Sturmfels: Cellular strings on polytopes
In: Proceedings of the American Mathematical Society, 122 (1994) 2, p. 549-555
Bibtex DOI: 10.2307/2161048

Billera, Louis J. and Bernd Sturmfels: Iterated fiber polytopes
In: Mathematika : a journal of pure and applied mathematics, 41 (1994) 2, p. 348-363
Bibtex DOI: 10.1112/S0025579300007440

Eisenbud, David and Bernd Sturmfels: Finding sparse systems of parameters
In: Journal of pure and applied algebra, 94 (1994) 2, p. 143-157
Bibtex DOI: 10.1016/0022-4049(94)90029-9 ARXIV: http://arxiv.org/abs/alg-geom/9305010

Onn, Shmuel and Bernd Sturmfels: A note on lattice simplices and toric varieties
In: American journal of mathematics, 116 (1994) 5, p. 1337-1339
Bibtex DOI: 10.2307/2374948

Onn, Shmuel and Bernd Sturmfels: A quantitative Steinitz' theorem
In: Beiträge zur Algebra und Geometrie, 35 (1994) 1, p. 125-129
Bibtex LINK: http://www.emis.de/journals/BAG/vol.35/no.1/

Sturmfels, Bernd: Viro's theorem for complete intersections
In: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 21 (1994) 3, p. 377-386
Bibtex LINK: http://www.numdam.org/item?id=ASNSP_1994_4_21_3_377_0

Sturmfels, Bernd: On the Newton polytope of the resultant
In: Journal of algebraic combinatorics : an international journal, 3 (1994) 2, p. 207-236
Bibtex DOI: 10.1023/A:1022497624378

Sturmfels, Bernd and Andrey V. Zelevinsky: Multigraded resultants of Sylvester type
In: Journal of algebra, 163 (1994) 1, p. 115-127
Bibtex DOI: 10.1006/jabr.1994.1007

Billera, Louis J. ; Gelfand, Izrail M. and Bernd Sturmfels: Duality and minors of secondary polyhedra
In: Journal of combinatorial theory / B, 57 (1993) 2, p. 258-268
Bibtex DOI: 10.1006/jctb.1993.1020

Bland, Robert G. ; Ko, Chun Wa and Bernd Sturmfels: A nonextremal Camion basis
In: Linear algebra and its applications, 187 (1993), p. 195-199
Bibtex DOI: 10.1016/0024-3795(93)90135-B

Gritzmann, Peter and Bernd Sturmfels: Minkowski addition of polytopes : computational complexity and applications to Gröbner bases
In: SIAM journal on discrete mathematics, 6 (1993) 2, p. 246-269
Bibtex DOI: 10.1137/0406019

Pedersen, Paul and Bernd Sturmfels: Product formulas for resultants and Chow forms
In: Mathematische Zeitschrift, 214 (1993) 1, p. 377-396
Bibtex DOI: 10.1007/BF02572411

Reeves, Alyson and Bernd Sturmfels: A note on polynomial reduction
In: Journal of symbolic computation, 16 (1993) 3, p. 273-277
Bibtex DOI: 10.1006/jsco.1993.1045

Sturmfels, Bernd and Andrey V. Zelevinsky: Maximal minors and their leading terms
In: Advances in mathematics, 98 (1993) 1, p. 65-112
Bibtex DOI: 10.1006/aima.1993.1013

Sturmfels, Bernd and Günter M. Ziegler: Extension spaces of oriented matroids
In: Discrete and computational geometry, 10 (1993) 1, p. 23-45
Bibtex DOI: 10.1007/BF02573961

Billera, Louis J. and Bernd Sturmfels: Fiber polytopes
In: Annals of mathematics, 135 (1992) 3, p. 527-549
Bibtex DOI: 10.2307/2946575

Kapranov, Mikhail M. ; Sturmfels, Bernd and Andrey V. Zelevinsky: Chow polytopes and general resultants
In: Duke mathematical journal, 67 (1992) 1, p. 189-218
Bibtex DOI: 10.1215/S0012-7094-92-06707-X

Logar, Alessandro and Bernd Sturmfels: Algorithms for the Quillen-Suslin theorem
In: Journal of algebra, 145 (1992) 1, p. 231-239
Bibtex DOI: 10.1016/0021-8693(92)90189-S

Sturmfels, Bernd: Asymptotic analysis of toric ideals
In: Memoirs of the faculty of science, Kyushu University. Series A : mathematics, 46 (1992) 2, p. 217-228
Bibtex DOI: 10.2206/kyushumfs.46.217

Kapranov, Mikhail M. ; Sturmfels, Bernd and Andrey V. Zelevinsky: Quotients of toric varieties
In: Mathematische Annalen, 290 (1991) 1, p. 643-655
Bibtex DOI: 10.1007/BF01459264

Kleinschmidt, Peter and Bernd Sturmfels: Smooth toric varieties with small Picard number are projective
In: Topology, 30 (1991) 2, p. 289-299
Bibtex DOI: 10.1016/0040-9383(91)90015-V

Richter, Jürgen and Bernd Sturmfels: On the topology and geometric construction of oriented matroids and convex polytopes
In: Transactions of the American Mathematical Society, 325 (1991) 1, p. 389-412
Bibtex DOI: 10.2307/2001676

Sturmfels, Bernd: Computational algebraic geometry of projective configurations
In: Journal of symbolic computation, 11 (1991) 5-6, p. 595-618
Bibtex DOI: 10.1016/S0747-7171(08)80121-6

Sturmfels, Bernd: Gröbner bases of toric varieties
In: Tohoku mathematical journal, 43 (1991) 2, p. 249-261
Bibtex DOI: 10.2748/tmj/1178227496

Sturmfels, Bernd and Neil L. White: Computing combinatorial decompositions of rings
In: Combinatorica, 11 (1991) 3, p. 275-293
Bibtex DOI: 10.1007/BF01205079

Sturmfels, Bernd and Neil L. White: Editorial
In: Journal of symbolic computation, 11 (1991) 5-6, p. 419-419
Bibtex DOI: 10.1016/S0747-7171(08)80112-5

Sturmfels, Bernd and Walter Whiteley: On the synthetic factorization of projectively invariant polynomials
In: Journal of symbolic computation, 11 (1991) 5-6, p. 439-453
Bibtex DOI: 10.1016/S0747-7171(08)80114-9

Bayer, Margaret and Bernd Sturmfels: Lawrence polytopes
In: Canadian journal of mathematics, 42 (1990) 1, p. 62-79
Bibtex DOI: 10.4153/CJM-1990-004-4

Billera, Louis J. ; Filliman, Paul and Bernd Sturmfels: Constructions and complexity of secondary polytopes
In: Advances in mathematics, 83 (1990) 2, p. 155-179
Bibtex DOI: 10.1016/0001-8708(90)90077-Z

Bokowski, Jürgen ; Richter, Jürgen and Bernd Sturmfels: Nonrealizability proofs in computational geometry
In: Discrete and computational geometry, 5 (1990) 4, p. 333-350
Bibtex DOI: 10.1007/BF02187794

Goodman, Jacob E. ; Pollack, Richard and Bernd Sturmfels: The intrinsic spread of a configuration in Rd
In: Journal of the American Mathematical Society, 3 (1990) 3, p. 639-651
Bibtex DOI: 10.2307/1990931

Gretenkort, Jörg ; Kleinschmidt, Peter and Bernd Sturmfels: On the existence of certain smooth toric varieties
In: Discrete and computational geometry, 5 (1990) 3, p. 255-262
Bibtex DOI: 10.1007/BF02187789

Sturmfels, Bernd: Gröbner bases and Stanley decompositions of determinantal rings
In: Mathematische Zeitschrift, 205 (1990) 1, p. 137-144
Bibtex DOI: 10.1007/BF02571229

Sturmfels, Bernd and Neil L. White: Stanley decompositions of the bracket ring
In: Mathematica Scandinavica, 67 (1990) 2, p. 183-189
Bibtex LINK: www.jstor.org/stable/24492662

Sturmfels, Bernd and Neil L. White: All 11 3 and 12 3 -configurations are rational
In: Aequationes mathematicae, 39 (1990) 2-3, p. 254-260
Bibtex DOI: 10.1007/BF01833153

Bokowski, Jürgen and Bernd Sturmfels: An infinite family of minor-minimal nonrealizable 3-chirotopes
In: Mathematische Zeitschrift, 200 (1989) 4, p. 583-589
Bibtex DOI: 10.1007/BF01160956

Havel, Timothy F. ; Sturmfels, Bernd and Neil L. White: Proposal for a geometric algebra software package
In: ACM SIGSAM bulletin, 23 (1989) 1, p. 13-15
Bibtex DOI: 10.1145/66062.66064

Jaggi, Beat ; Mani-Levitska, Peter ; Sturmfels, Bernd and Neil L. White: Uniform oriented matroids without the isotopy property
In: Discrete and computational geometry, 4 (1989) 2, p. 97-100
Bibtex DOI: 10.1007/BF02187717

Ljubic, Dragoslav ; Roudneff, Jean-Pierre and Bernd Sturmfels: Arrangements of lines and pseudolines without adjacent triangles
In: Journal of combinatorial theory / A, 50 (1989) 1, p. 24-32
Bibtex DOI: 10.1016/0097-3165(89)90003-4

Sturmfels, Bernd: On the matroid stratification of Grassmann varieties, specialization of coordinates, and a problem of N. White
In: Advances in mathematics, 75 (1989) 2, p. 202-211
Bibtex DOI: 10.1016/0001-8708(89)90037-6

Sturmfels, Bernd: Computing final polynomials and final syzygies using Buchberger's Gröbner bases method
In: Results in mathematics, 15 (1989) 3-4, p. 351-360
Bibtex DOI: 10.1007/BF03322623

Sturmfels, Bernd: Dynamic versions of the Buchberger algorithm
In: RISC-Linz series : publications, reports (The Research Institute for Symbolic Computation), 1989 (1989), 89-16
Bibtex

White, Neil L. and Bernd Sturmfels: Gröbner bases and invariant theory
In: Advances in mathematics, 76 (1989) 2, p. 245-259
Bibtex DOI: 10.1016/0001-8708(89)90053-4

Roudneff, Jean-Pierre and Bernd Sturmfels: Simplicial cells in arrangements and mutations of oriented matroids
In: Geometriae dedicata, 27 (1988) 2, p. 153-170
Bibtex DOI: 10.1007/BF00151346

Sturmfels, Bernd: Neighborly polytopes and oriented matroids
In: European journal of combinatorics, 9 (1988) 6, p. 537-546
Bibtex DOI: 10.1016/S0195-6698(88)80050-7

Sturmfels, Bernd: Tridiagonalization of complex matrices and a problem of Longstaff
In: Linear algebra and its applications, 109 (1988), p. 165-166
Bibtex DOI: 10.1016/0024-3795(88)90207-8

Sturmfels, Bernd: Totally positive matrices and cyclic polytopes
In: Linear algebra and its applications, 107 (1988), p. 275-281
Bibtex DOI: 10.1016/0024-3795(88)90250-9

Sturmfels, Bernd: Some applications of affine Gale diagrams to polytopes with few vertices
In: SIAM journal on discrete mathematics, 1 (1988) 1, p. 121-133
Bibtex DOI: 10.1137/0401014

Bokowski, Jürgen and Bernd Sturmfels: Polytopal and nonpolytopal spheres an algorithmic approach
In: Israel journal of mathematics, 57 (1987) 3, p. 257-271
Bibtex DOI: 10.1007/BF02766213

Sturmfels, Bernd: Cyclic polytopes and d-order curves
In: Geometriae dedicata, 24 (1987) 1, p. 103-107
Bibtex DOI: 10.1007/BF00159750

Sturmfels, Bernd: Boundary complexes of convex polytopes cannot be characterized locally
In: The journal of the London Mathematical Society, 35 (1987) 2, p. 314-326
Bibtex DOI: 10.1112/jlms/s2-35.2.314

Sturmfels, Bernd: On the decidability of Diophantine problems in combinatorial geometry
In: Bulletin of the American Mathematical Society, 17 (1987) 1, p. 121-124
Bibtex DOI: 10.1090/S0273-0979-1987-15532-7

Bokowski, Jürgen and Bernd Sturmfels: On the coordinatization of oriented matroids
In: Discrete and computational geometry, 1 (1986) 4, p. 293-306
Bibtex DOI: 10.1007/BF02187702

Sturmfels, Bernd: Central and parallel projections of polytopes
In: Discrete mathematics, 62 (1986) 3, p. 315-318
Bibtex DOI: 10.1016/0012-365X(86)90220-7

Publications in Books and Conference Proceedings

Kulkarni, Avinash ; Ren, Yue ; Sayyary Namin, Mahsa and Bernd Sturmfels: Real space sextics and their tritangents
In: ISSAC '18 proceedings of the 43rd international symposium on symbolic and algebraic computation ; New York, USA, July 16-19, 2018
New York : ACM, 2018. - P. 247-254
Bibtex MIS-Preprint: 81/2017 DOI: 10.1145/3208976.3208977 ARXIV: https://arxiv.org/abs/1712.06274

Abo, Hirotachi ; Seigal, Anna and Bernd Sturmfels: Eigenconfigurations of tensors
In: Algebraic and geometric methods in discrete mathematics / Heather A.Harrington... (eds.)
Providence, Rhode Island : American Mathematical Society, 2017. - P. 1-25
(Contemporary mathematics ; 685)
Bibtex DOI: 10.1090/conm/685/13717 ARXIV: http://arxiv.org/abs/1505.05729

Kubjas, Kaie ; Parrilo, Pablo A. and Bernd Sturmfels: How to flatten a soccer ball
In: Homological and computational methods in commutative algebra : dedicated to Winfried Bruns on the occasion of his 70th birthday / AldoConca... (eds.)
Cham : Springer, 2017. - P. 141-162
(Springer INdAM series ; 20)
Bibtex DOI: 10.1007/978-3-319-61943-9_9 ARXIV: http://arxiv.org/abs/1606.02253

Kukelova, Zuzana ; Kileel, Joe ; Sturmfels, Bernd and Tomas Pajdla: A clever elimination strategy for efficient minimal solvers
In: 30th IEEE conference on computer vision and pattern recognition CVPR 2017, 21-26 July 2017 Honolulu, Hawaii : proceedings / RamaChellappa... (eds.)
Piscataway, NJ : IEEE, 2017. - P. 3605-3614
Bibtex DOI: 10.1109/CVPR.2017.384 ARXIV: https://arxiv.org/abs/1703.05289

Sturmfels, Bernd: Fitness, apprenticeship, and polynomials
In: Combinatorial algebraic geometry : selected papers from the 2016 apprenticeship program / BerndSturmfels... (eds.)
New York : Springer, 2017. - P. 1-19
(Fields Institute communications ; 80)
Bibtex DOI: 10.1007/978-1-4939-7486-3_1 ARXIV: https://arxiv.org/abs/1612.03539

Trager, Matthew ; Sturmfels, Bernd ; Canny, John ; Hebert, Martial and Jean Ponce: General models for rational cameras and the case of two-slit projections
In: 30th IEEE conference on computer vision and pattern recognition CVPR 2017, 21-26 July 2017 Honolulu, Hawaii : proceedings / RamaChellappa... (eds.)
Piscataway, NJ : IEEE, 2017. - P. 2520-2528
Bibtex DOI: 10.1109/CVPR.2017.270 ARXIV: https://arxiv.org/abs/1612.01160

Améndola, Carlos ; Drton, Mathias and Bernd Sturmfels: Maximum likelihood estimates for Gaussian mixtures are transcendental
In: Mathematical aspects of computer and information sciences : 6th international conference, MACIS 2015, Berlin, Germany, November 11-13, 2015, revised selected papers / Ilias S.Kotsireas... (eds.)
Cham : Springer, 2016. - P. 579-590
(Lecture notes in computer science ; 9582)
Bibtex DOI: 10.1007/978-3-319-32859-1_49 ARXIV: http://arxiv.org/abs/1508.06958

Bürgisser, Peter ; Kohn, Kathlén ; Lairez, Pierre and Bernd Sturmfels: Computing the Chow variety of quadratic space curves
In: Mathematical aspects of computer and information sciences : 6th international conference, MACIS 2015, Berlin, Germany, November 11-13, 2015, revised selected papers / Ilias S.Kotsireas... (eds.)
Cham : Springer, 2016. - P. 130-136
(Lecture notes in computer science ; 9582)
Bibtex DOI: 10.1007/978-3-319-32859-1_10 ARXIV: http://arxiv.org/abs/1508.07219

Draisma, Jan ; Horobet, Emil ; Ottaviani, Giorgio ; Sturmfels, Bernd and Rekha R. Thomas: The Euclidean distance degree
In: SNC 2014 : proceedings of the 2014 symposium on symbolic-numeric computation : July 28-31, 2014, Shanghai, China / Stephen M.Watt (ed.)
New York : ACM, 2014. - P. 9-16
Bibtex DOI: 10.1145/2631948.2631951

Huh, June and Bernd Sturmfels: Likelihood geometry
In: Combinatorial algebraic geometry : lecture notes from the CIME-CIRM summer school held in Levico Terme, June 10-15, 2013 / AldoConca... (eds.)
New York : Springer, 2014. - P. 63-117
(Lecture notes in mathematics ; 2108)
Bibtex DOI: 10.1007/978-3-319-04870-3_3 ARXIV: http://arxiv.org/abs/1305.7462

Sturmfels, Bernd: Maximum likelihood for matrices with rank constraints : [invited talk abstract]
In: ISSAC '14 proceedings of the 39th international symposium on symbolic and algebraic computation ; Kobe, Japan July 23-25, 2014 / KatsusukeNabeshima (ed.)
New York : ACM, 2014. - P. 17-17
Bibtex DOI: 10.1145/2608628.2627490

Chan, Melody and Bernd Sturmfels: Elliptic curves in honeycomb form
In: Algebraic and combinatorial aspects of tropical geometry / ErwanBrugallé... (eds.)
Providence, R.I. : American Mathematical Society, 2013. - P. 87-107
(Contemporary mathematics ; 589)
Bibtex DOI: 10.1090/conm/589/11743 ARXIV: http://arxiv.org/abs/1203.2356

Rostalski, Philipp and Bernd Sturmfels: Dualities
In: Semidefinite optimization and convex algebraic geometry / GrigoriyBlekherman... (eds.)
Philadelphia : Society for Industrial and Applied Mathematics, 2013. - P. 203-249
(MOS-SIAM series on optimization ; 13)
Bibtex

Plaumann, Daniel ; Sturmfels, Bernd and Cynthia Vinzant: Computing linear matrix representations of Helton-Vinnikov curves
In: Mathematical methods in systems, optimization, and control : Festschrift in honor of J. William Helton / HarryDym... (eds.)
Basel : Springer, 2012. - P. 259-277
(Operator theory : advances and applications ; 222)
Bibtex DOI: 10.1007/978-3-0348-0411-0_19 ARXIV: http://arxiv.org/abs/1011.6057

Ranestad, Kristian and Bernd Sturmfels: The convex hull of a variety
In: Notions of positivity and the geometry of polynomials / PetterBrändén... (eds.)
Basel : Birkhäuser, 2011. - P. 331-344
(Trends in mathematics)
Bibtex DOI: 10.1007/978-3-0348-0142-3_18 ARXIV: http://arxiv.org/abs/1004.3018

Riegler, Erwin ; Morgenshtern, Veniamin I. ; Durisi, Giuseppe ; Lin, Shaowei ; Sturmfels, Bernd and Helmut Bölcskei: Noncoherent SIMO pre-log via resolution of singularities
In: IEEE international symposium on information theory proceedings (ISIT) 2011 : July 31-August 5, 2011 in St. Petersburg, Russia
Piscataway, NY : IEEE, 2011. - P. 2020-2024
Bibtex DOI: 10.1109/ISIT.2011.6033909 ARXIV: http://arxiv.org/abs/1105.6009

Cueto, Maria Angélica ; Morton, Jason and Bernd Sturmfels: Geometry of the restricted Boltzmann machine
In: Algebraic methods in statistics and probability : volume 2 / Marlos A. G.Viana... (eds.)
Providence, R.I. : American Mathematical Society, 2010. - P. 135-153
(Contemporary mathematics ; 516)
Bibtex DOI: 10.1090/conm/516/10172 ARXIV: http://arxiv.org/abs/0908.4425

Sturmfels, Bernd: Open problems in algebraic statistics
In: Emerging applications of algebraic geometry / MihaiPutinar... (eds.)
New York : Springer, 2009. - P. 351-363
(The IMA volumes in mathematics and its applications ; 149)
Bibtex DOI: 10.1007/978-0-387-09686-5_10 ARXIV: http://arxiv.org/abs/0707.4558

Nie, Jiawang ; Parrilo, Pablo A. and Bernd Sturmfels: Semidefinite representation of the \({k}\)-ellipse
In: Algorithms in algebraic geometry / AliciaDickenstein... (eds.)
New York : Springer, 2008. - P. 117-132
(The IMA volumes in mathematics and its applications ; 146)
Bibtex DOI: 10.1007/978-0-387-75155-9_7 ARXIV: http://arxiv.org/abs/math/0702005

Sturmfels, Bernd and Josephine Yu: Tropical implicitization and mixed fiber polytopes
In: Software for algebraic geometry / Michael E.Stillman... (eds.)
New York : Springer, 2008. - P. 111-131
(The IMA volumes in mathematics and its applications ; 148)
Bibtex DOI: 10.1007/978-0-387-78133-4_7 ARXIV: http://arxiv.org/abs/0706.0564

Fotiou, Ioannis A. ; Rostalski, Philipp ; Sturmfels, Bernd and Manfred Morari: An algebraic geometry approach to nonlinear parametric optimization in control
In: Proceedings of the 2006 american control conference : Minneapolis, Minnesota, USA, June 14-16, 2006
New York : IEEE, 2006. - P. 3618-3623
Bibtex DOI: 10.1109/ACC.2006.1657280 ARXIV: http://arxiv.org/abs/math/0509288

Morton, Jason ; Pachter, Lior ; Shiu, Anne ; Sturmfels, Bernd and Oliver Wienand: Geometry of rank tests
In: Proceedings of the third european workshop on probabilistic graphical models : Prague, Czech Republic, September 12-15, 2006 / MilanStudeny... (eds.)
Prague : Agentura Action M, 2006
Bibtex ARXIV: http://arxiv.org/abs/math/0605173 LINK: http://www.utia.cas.cz/pgm06_proceedings

Develin, Mike ; Santos, Francisco and Bernd Sturmfels: On the rank of a tropical matrix
In: Combinatorial and computational geometry / Jacob EliGoodman... (eds.)
Cambridge : Cambridge University Press, 2005. - P. 213-242
(Mathematical sciences research institute publications ; 52)
Bibtex ARXIV: http://arxiv.org/abs/math/0312114

Eriksson, Nicholas ; Ranestad, Kristian ; Sturmfels, Bernd and Seth Sullivant: Phylogenetic algebraic geometry
In: Projective varieties with unexpected properties : a volume in memory of Giuseppe Veronese ; proceedings of the international conference 'Varieties with Unexpected Properties', Siena, Italy, June 8-13, 2004 / CiroCiliberto... (eds.)
Berlin : de Gruyter, 2005. - P. 237-255
Bibtex DOI: 10.1515/9783110199703.237 ARXIV: http://arxiv.org/abs/math/0407033

Pachter, Lior and Bernd Sturmfels: Statistics [chapter 1]
In: Algebraic statistics for computational biology / LiorPachter... (eds.)
Cambridge : Cambridge University Press, 2005. - P. 3-42
Bibtex DOI: 10.1017/CBO9780511610684.004

Pachter, Lior and Bernd Sturmfels: Computation [chapter 2]
In: Algebraic statistics for computational biology / LiorPachter... (eds.)
Cambridge : Cambridge University Press, 2005. - P. 43-84
Bibtex DOI: 10.1017/CBO9780511610684.005

Pachter, Lior and Bernd Sturmfels: Algebra [chapter 3]
In: Algebraic statistics for computational biology / LiorPachter... (eds.)
Cambridge : Cambridge University Press, 2005. - P. 85-124
Bibtex DOI: 10.1017/CBO9780511610684.006

Pachter, Lior and Bernd Sturmfels: Preface
In: Algebraic statistics for computational biology / LiorPachter... (eds.)
Cambridge : Cambridge University Press, 2005
Bibtex DOI: 10.1017/CBO9780511610684.001

Richter-Gebert, Jürgen ; Sturmfels, Bernd and Thorsten Theobald: First steps in tropical geometry
In: Idempotent mathematics and mathematical physics : international workshop February 3-10, 2003 Erwin Schrödinger international institute for mathematical physics Vienna, Austria / Grigory L.Litvinov... (eds.)
Providence, R.I. : American Mathematical Society, 2005. - P. 289-317
(Contemporary mathematics ; 377)
Bibtex DOI: 10.1090/conm/377/06998 ARXIV: http://arxiv.org/abs/math/0306366

Sturmfels, Bernd: Algebraic recipes for integer programming
In: Trends in Optimization / SerkanHosten... (eds.)
Providence, R.I. : American Mathematical Society, 2004. - P. 99-113
(Proceedings of symposia in applied mathematics ; 61)
Bibtex DOI: 10.1090/psapm/061/2104733 ARXIV: https://arxiv.org/abs/math/0310194

Parrilo, Pablo A. and Bernd Sturmfels: Minimizing polynomial functions
In: Algorithmic and quantitative real algebraic geometry : proceedings of the DIMACS workshop on algorithmic and quantitative aspects of real algebraic geometry in mathematics and computer science, DIMACS Center, March 12-16, 2001 / SaugataBasu... (eds.)
Providence, R.I. : American Mathematical Society, 2003. - P. 83-99
(Series in discrete mathematics and theoretical computer science ; 60)
Bibtex ARXIV: https://arxiv.org/abs/math/0103170

Geiger, Dan ; Meek, Christopher and Bernd Sturmfels: Factorization of discrete probability distributions
In: Uncertainty in artificial intelligence : proceedings of the eighteenth conference (2002) ; August 1-4, 2002, University of Alberta, Edmonton / AdnanDarwiche (ed.)
San Francisco : Morgan Kaufmann, 2002. - P. 162-169
Bibtex ARXIV: http://de.arxiv.org/abs/1301.0568

Smith, Gregory G. and Bernd Sturmfels: Teaching the geometry of schemes
In: Computations in algebraic geometry with Macaulay 2 / DavidEisenbud... (eds.)
Berlin : Springer, 2002. - P. 55-70
(Algorithms and computation in mathematics ; 8)
Bibtex DOI: 10.1007/978-3-662-04851-1_4 ARXIV: http://de.arxiv.org/abs/math/0003033

Stillman, Michael E. ; Sturmfels, Bernd and Rekha R. Thomas: Algorithms for the toric Hilbert scheme
In: Computations in algebraic geometry with Macaulay 2 / DavidEisenbud... (eds.)
Berlin : Springer, 2002. - P. 179-214
(Algorithms and computation in mathematics ; 8)
Bibtex DOI: 10.1007/978-3-662-04851-1_8 ARXIV: https://arxiv.org/abs/math/0010130

Sturmfels, Bernd: Ideals, varieties and Macaulay 2
In: Computations in algebraic geometry with Macaulay 2 / DavidEisenbud... (eds.)
Berlin : Springer, 2002. - P. 3-15
(Algorithms and computation in mathematics ; 8)
Bibtex DOI: 10.1007/978-3-662-04851-1_1

Sturmfels, Bernd: Gröbner bases of abelian matrix groups
In: Symbolic computation : solving equations in algebra, geometry, and engineering / Edward L.Green... (eds.)
Providence, R.I. : American Mathematical Society, 2001. - P. 141-143
(Contemporary mathematics ; 286)
Bibtex DOI: 10.1090/conm/286/04760

Miller, Ezra and Bernd Sturmfels: Monomial ideals and planar graphs
In: Applied algebra, algebraic algorithms and error-correcting codes : 13th international symposium, AAECC-13 Honolulu, Hawaii, USA, November 15-19, 1999 proceedings / MarcFossorier... (eds.)
Berlin : Springer, 1999. - P. 19-28
(Lecture notes in computer science ; 1719)
Bibtex DOI: 10.1007/3-540-46796-3_3

Sturmfels, Bernd: The Co-Scarf resolution
In: Commutative algebra, algebraic geometry, and computational methods : proceedings of the conference on algebraic geometry, commutative algebra, and computation, Hanoi, Vietnam, 1996 / DavidEisenbud (ed.)
Singapore : Springer, 1999. - P. 315-320
Bibtex

Diaconis, Persi ; Eisenbud, David and Bernd Sturmfels: Lattice walks and primary decomposition
In: Mathematical essays in honor of Gian-Carlo Rota / Bruce EliSagan... (eds.)
Boston : Birkhäuser, 1998. - P. 173-193
(Progress in mathematics ; 161)
Bibtex DOI: 10.1007/978-1-4612-4108-9_8

Sturmfels, Bernd: Introduction to resultants
In: Applications of computational algebraic geometry : lectures presented at the American Mathematical Society ; short course held in San Diego, CA, January 6-7, 1997 / David A.Cox... (eds.)
Providence, R.I. : American Mathematical Society, 1998. - P. 25-39
(Proceedings of symposia in applied mathematics ; 53)
Bibtex DOI: 10.1090/psapm/053/1602347

Sturmfels, Bernd and Nobuki Takayama: Gröbner bases and hypergeometric functions
In: Gröbner bases and applications : [Proceedings of the conference 33 years of Gröbner bases] / BrunoBuchberger... (eds.)
Cambridge : Cambridge University Press, 1998. - P. 246-258
(London Mathematical Society lecture note series ; 251)
Bibtex

Sturmfels, Bernd: Equations defining toric varieties
In: Algebraic geometry Santa Cruz 1995
Providence, R.I. : American Mathematial Society, 1997. - P. 437-449
(Proceedings of symposia in pure mathematics ; 62.2)
Bibtex DOI: 10.1090/pspum/062.2/1492542 ARXIV: https://arxiv.org/abs/alg-geom/9610018

Cattani, Eduardo ; Dickenstein, Alicia and Bernd Sturmfels: Computing multidimensional residues
In: Algorithms in algebraic geometry and applications / LaureanoGonzalez-Vega... (eds.)
Basel : Birkhäuser, 1996. - P. 135-164
(Progress in mathematics ; 143)
Bibtex DOI: 10.1007/978-3-0348-9104-2_8 ARXIV: https://arxiv.org/abs/alg-geom/9404011v1

Diaconis, Persi ; Graham, Ronald L. and Bernd Sturmfels: Primitive partition identities
In: Combinatorics, Paul Erdos is eighty (Vol. 2) / DézsoMiklós... (eds.)
Budapest : János Bolyai Mathematical Society, 1996. - P. 173-192
(Bolyai Society Mathematical studies ; 2)
Bibtex LINK: https://oeis.org/A007343/a007343.pdf

Pedersen, Paul and Bernd Sturmfels: Mixed monomial bases
In: Algorithms in algebraic geometry and applications / LaureanoGonzalez-Vega... (eds.)
Basel : Birkhäuser, 1996. - P. 307-316
(Progress in mathematics ; 143)
Bibtex DOI: 10.1007/978-3-0348-9104-2_15

Dalbec, John and Bernd Sturmfels: Introduction to Chow forms
In: Invariant methods in discrete and computational geometry : proceedings of the Curacao conference, 13-17 June, 1994 / Neil L.White (ed.)
Dordrecht : Kluwer Academic, 1995. - P. 37-58
Bibtex DOI: 10.1007/978-94-015-8402-9_2

Hosten, Serkan and Bernd Sturmfels: GRIN : an implementation of Gröbner bases for integer programming
In: Integer programming and combinatorial optimization : 4th International IPCO Conference Copenhagen, Denmark, May 29-31, 1995 : proceedings / EgonBalas (ed.)
Berlin : Springer, 1995. - P. 267-276
(Lecture notes in computer science ; 920)
Bibtex DOI: 10.1007/3-540-59408-6_57

Sturmfels, Bernd: On the number of real roots of a sparse polynomial system
In: Hamiltonian and gradient flows, algorithms and control / AnthonyBloch (ed.)
Providence, R.I. : American Mathematical Society, 1994. - P. 137-143
(Fields Institute communications ; 3)
Bibtex

Sturmfels, Bernd and Josephine Yu: Minimal polynomials and sparse resultants
In: Zero-dimensional schemes : proceedings of the international conference held in Ravello, June 8- 3, 1992 / FerruccioOrecchia (ed.)
Berlin : de Gruyter, 1994. - P. 317-324
Bibtex

Sturmfels, Bernd: Sparse elimination theory
In: Computational algebraic geometry and commutative algebra : proceedings of a conference held at Cortona, Italy, June 17-21, 1991 / DavidEisenbud (ed.)
Cambridge : Cambridge University Press, 1993. - P. 264-298
(Symposia mathematica ; 34)
Bibtex

Kleinschmidt, Peter ; Schwartz, Niels and Bernd Sturmfels: Unimodular fans, linear codes, and toric manifolds
In: Discrete and computational geometry : papers from the DIMACS special year / Jacob EliGoodman... (eds.)
Providence, R. I. : American Mathematical Society, 1991. - P. 179-186
(DIMACS series in discrete mathematics and theoretical computer science ; 6)
Bibtex

Rota, Gian-Carlo and Bernd Sturmfels: Introduction to invariant theory in superalgebras
In: Invariant theory and tableaux : [workshop on invariant theory and tableaux held at the IMA on March 21-25, 1988] / DennisStanton (ed.)
New York : Springer, 1990. - P. 1-35
(The IMA volumes in mathematics and its applications ; 19)
Bibtex

Goodman, Jacob E. ; Pollack, Richard and Bernd Sturmfels: Coordinate representation of order types requires exponential storage
In: Proceedings of the twenty-first annual ACM symposium on theory of computing : Seattle, 1989
New York : ACM, 1989. - P. 405-410
Bibtex DOI: 10.1145/73007.73046

Sturmfels, Bernd: Aspects of computational synthetic geometry : I. Algorithmic coordinatization of matroids
In: Computer-aided geometric reasoning : workshop, 22-26 juin 1987, INRIA Sophia-Antipolis (France) : volume 1. / Henry H.Crapo (ed.)
Le Chesnay : INRIA, 1987. - P. 57-86
Bibtex

Bokowski, Jürgen and Bernd Sturmfels: Reell realisierbare orientierte Matroide
In: Diskrete Strukturen, algebraische Methoden und Anwendungen : 2. Sommerschule Diskrete Strukturen, Bayreuth, 1985 / AdalbertKerber (ed.)
Bayreuth : Universitat Bayreuth, 1986. - P. 1-13
(Bayreuther mathematische Schriten ; 21)
Bibtex

Preprints

Améndola, Carlos ; Sturmfels, Bernd and Peter Friz: Varieties of signature tensors

Baletti, Gabriele ; Sturmfels, Bernd and Marta Panizzut: K3 polytopes and their quartic surfaces

Cifuentes, Diego ; Harris, Corey and Bernd Sturmfels: The geometry of SDP-exactness in quadratic optimization

Cifuentes, Diego ; Ranestad, Kristian ; Sturmfels, Bernd and Madeleine Weinstein: Voronoi cells of varieties

Kohn, Kathlén ; Shapiro, Boris and Bernd Sturmfels: Moment varieties of measures on polytopes

Löhne, Andreas ; Ciripoi, Daniel ; Kaihnsa, Nidhi and Bernd Sturmfels: Computing convex hulls of trajectories

Pfeffer, Max ; Seigal, Anna and Bernd Sturmfels: Learning paths from signature tensors

Robeva, Elina ; Sturmfels, Bernd ; Tran, Ngoc Mai and Caroline Uhler: Maximum likelihood estimation for totally positive log-concave densities

Chua, Lynn ; Kummer, Mario and Bernd Sturmfels: Schottky algorithms : classical meets tropical

Robeva, Elina ; Sturmfels, Bernd and Caroline Uhler: Geometry of log-concave density estimation

Lin, Bo ; Sturmfels, Bernd ; Tang, Xiaoxian and Ruriko Yoshida: Appendix for 'Convexity in tree spaces'

Agarwal, Sameer ; Lee, Hon-Leung ; Sturmfels, Bernd and Rekha R. Thomas: Certifying the existence of epipolar matrices

Lin, Shaowei ; Oeding, Luke and Bernd Sturmfels: Electric network synthesis

Schweighofer, Markus ; Sturmfels, Bernd and Rekha R. Thomas: Convex algebraic geometry

De Loera, Jesús A. and Bernd Sturmfels: Counting network flows

Sturmfels, Bernd: The geometry of A-graded algebras

Billera, Louis J. ; Kapranov, Mikhail M. and Bernd Sturmfels: On a conjecture of Baues in the theory of loop spaces

Crapo, Henry H. ; Havel, Timothy F. ; Sturmfels, Bernd ; Whiteley, Walter and Neil L. White: Symbolic computations in geometry

Sturmfels, Bernd: An algorithmic proof of the Quillen-Suslin theorem

Sturmfels, Bernd: Simplicial polytopes without the isotopy property

Sturmfels, Bernd and Neil L. White: Constructing uniform oriented matroids without the isotopy property

Sturmfels, Bernd: Applications of final polynomials and final syzygies

Bokowski, Jürgen and Bernd Sturmfels: Programmsystem zur Realisierung orientierter Matroide

Academic Theses

Sturmfels, Bernd: Oriented matroids and combinatorial convex geometry
Dissertation, Technische Hochschule Darmstadt, 1987
Bibtex

Books

Smith, Gregory G. and Bernd Sturmfels (eds.): Combinatorial algebraic geometry : selected papers from the 2016 apprenticeship program
New York : Springer, 2017. - VIII, 390 p.
(Fields Institute communications ; 80)
ISBN 978-1-4939-7486-3 ISBN 978-1-4939-7485-6
Bibtex DOI: 10.1007/978-1-4939-7486-3

Maclagan, Diane and Bernd Sturmfels: Introduction to tropical geometry
Providence, R.I. : American Mathematical Society, 2015. - XII, 363 p.
(Graduate studies in mathematics ; 161)
ISBN 978-0-8218-5198-2
Bibtex

Conca, Aldo ; Di Rocco, Sandra ; Draisma, Jan ; Huh, June ; Sturmfels, Bernd and Filippo Viviani (eds.): Combinatorial algebraic geometry : lecture notes from the CIME-CIRM summer school held in Levico Terme, June 10-15, 2013
Cham : Springer, 2014. - VII, 239 p.
(Lecture notes in mathematics ; 2108)
ISBN 978-3-319-04870-3 ISBN 978-3-319-04869-7
Bibtex DOI: 10.1007/978-3-319-04870-3

Avramov, Luchezar L. ; Green, Mark ; Huneke, Craig ; Smith, Karen E. and Bernd Sturmfels (eds.): Trends in commutative algebra : [Based on lectures presented at the MSRI introductory workshop on commutative algebra held at the Mathematical Sciences Research Institute, Berkeley, CA, USA, September 9-13, 2002]
Reprint of the 2004 hardback edition. - New York : Cambridge University Press, 2011. - X, 254 p.
(Mathematical sciences research institute publications ; 51)
ISBN 978-0-521-16872-4 ISBN 978-0-511-15945-9
Bibtex

Drton, Mathias ; Sturmfels, Bernd and Seth Sullivant: Lectures on algebraic statistics
Boston, MA : Birkhäuser, 2009. - VIII, 171 p.
(Oberwolfach seminars ; 39)
ISBN 978-3-7643-8904-8 ISBN 978-3-7643-8905-5
Bibtex DOI: 10.1007/978-3-7643-8905-5

Sturmfels, Bernd: Algorithms in invariant theory
Second edition. - Wien : Springer, 2008. - 197 p.
(Texts and monographs in symbolic computation)
ISBN 978-3-211-77416-8 ISBN 978-3-211-77417-5
Bibtex DOI: 10.1007/978-3-211-77417-5

Miller, Ezra ; Reiner, Victor and Bernd Sturmfels (eds.): Geometric combinatorics : lectures from the graduate summer school held in Park City, UT, 2004
Providence, R.I. : American Mathematical Society, 2007. - XII, 691 p.
(IAS/Park City mathematics series ; 13)
ISBN 978-0-8218-3736-8 ISBN 0-8218-3736-2
Bibtex

Miller, Ezra and Bernd Sturmfels: Combinatorial commutative algebra
New York : Springer, 2005. - XIV, 417 p.
(Graduate texts in mathematics ; 227)
ISBN 978-0-387-22356-8 ISBN 978-0-387-27103-3 ISBN 0-387-22356-8
Bibtex DOI: 10.1007/b138602

Pachter, Lior and Bernd Sturmfels (eds.): Algebraic statistics for computational biology
Cambridge : Cambridge University Press, 2005. - XII, 420 p.
ISBN 0-521-85700-7 ISBN 978-0-521-85700-0
Bibtex DOI: 10.1017/CBO9780511610684

Avramov, Luchezar L. ; Green, Mark ; Huneke, Craig ; Smith, Karen E. and Bernd Sturmfels (eds.): Trends in commutative algebra : [Based on lectures presented at the MSRI introductory workshop on commutative algebra held at the Mathematical Sciences Research Institute, Berkeley, CA, USA, September 9-13, 2002]
New York : Cambridge University Press, 2004. - X, 254 p.
(Mathematical sciences research institute publications ; 51)
ISBN 978-0-521-83195-6 ISBN 978-0-521-16872-4 ISBN 0-521-83195-4 ISBN 0-511-15945-5
Bibtex

Eisenbud, David ; Grayson, Daniel R. ; Stillman, Michael E. and Bernd Sturmfels (eds.): Computations in algebraic geometry with Macaulay 2
Berlin : Springer, 2002. - XIII, 329 p.
(Algorithms and computation in mathematics ; 8)
ISBN 978-3-642-07592-6 ISBN 978-3-662-04851-1 ISBN 3-540-42230-7
Bibtex DOI: 10.1007/978-3-662-04851-1

Sturmfels, Bernd: Solving systems of polynomial equations
Providence, R.I. : American Mathematical Society, 2002. - VIII, 152 p.
(CBMS regional conference series in mathematics ; 97)
ISBN 978-0-8218-3251-6 ISBN 978-1-4704-2457-2 ISBN 0-8218-3251-4
Bibtex DOI: 10.1090/cbms/097

Saito, Mutsumi ; Sturmfels, Bernd and Nobuki Takayama: Gröbner deformations of hypergeometric differential equations
Berlin : Springer, 2000. - VIII, 254 p.
(Algorithms and computation in mathematics ; 6)
ISBN 978-3-642-08534-5 ISBN 978-3-662-04112-3
Bibtex DOI: 10.1007/978-3-662-04112-3

Björner, Anders ; Las Vergnas, Michel ; Sturmfels, Bernd ; White, Neil L. and Günter M. Ziegler (eds.): Oriented matroids
Second edtion. - Cambridge : Cambridge University Press, 1999. - XII, 548 p.
(Encyclopedia of mathematics and its applications ; 46)
ISBN 0-521-77750-x ISBN 978-0-521-77750-6 ISBN 978-0-511-89363-6
Bibtex

Cox, David A. and Bernd Sturmfels (eds.): Applications of computational algebraic geometry : lectures presented at the American Mathematical Society ; short course held in San Diego, CA, January 6-7, 1997
Providence, R.I. : American Mathematical Society, 1998. - IX, 172 p.
(Proceedings of symposia in applied mathematics ; 53)
ISBN 978-0-8218-0750-7 ISBN 978-0-8218-9268-8 ISBN 0-8218-0750-1
Bibtex DOI: 10.1090/psapm/053

Sturmfels, Bernd: Gröbner bases and convex polytopes
Providence, R.I. : American Mathematical Society, 1996. - XI, 162 p.
(University lecture series ; 8)
ISBN 0-8218-0487-1 ISBN 978-1-4704-9787-1 ISBN 978-0-8218-0487-2
Bibtex DOI: 10.1090/ulect/008

Björner, Anders ; Las Vergnas, Michel ; Sturmfels, Bernd ; White, Neil L. and Günter M. Ziegler (eds.): Oriented matroids
Cambridge : Cambridge University Press, 1993. - XII, 516 p.
(Encyclopedia of mathematics and its applications ; 46)
ISBN 0-521-41836-4
Bibtex

Hilbert, David ; Sturmfels, Bernd and Reinhard Laubenbacher: Theory of algebraic invariants
Cambridge : Cambridge University Press, 1993. - XIV, 191 p.
(Cambridge mathematical library)
ISBN 0-521-44903-0 ISBN 0-521-44457-8
Bibtex

Sturmfels, Bernd: Algorithms in invariant theory
Wien : Springer, 1993. - 197 p.
(Texts and monographs in symbolic computation)
ISBN 0-387-82445-6 ISBN 3-211-82445-6
Bibtex

Gritzmann, Peter and Bernd Sturmfels (eds.): Applied geometry and discrete mathematics : the Victor Klee Festschrift
Providence, R. I. : American Mathematical Society, 1991. - XL, 608 p.
(DIMACS series in discrete mathematics and theoretical computer science ; 4)
ISBN 0-8218-6593-5 ISBN 0-89791-385-x
Bibtex

Bokowski, Jürgen and Bernd Sturmfels: Computational synthetic geometry
Berlin : Springer, 1989. - 168 p.
(Lecture notes in mathematics ; 1355)
ISBN 978-3-540-50478-8 ISBN 978-3-540-46013-8
Bibtex DOI: 10.1007/BFb0089253

Sturmfels, Bernd: Computational synthetic geometry
Berlin : Springer, 1987. - 141 p. Bibtex

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