283.
Pencils of Quadrics: Old and New (with Claudia Fevola
and Yelena Mandelshtam),
15pp, submitted to Le Matematiche.
282.
Bad Projections of the PSD Cone (with Yuhan Jiang),
18pp, submitted to Collectanea Mathematica.
281.
The Dubrovin Threefold of an Algebraic Curve (with
Daniele Agostini and Türkü Özlüm Çelik),
28pp, submitted to Nonlinearity.
280.
Wasserstein Distance to Independence Models
(with Türkü Özlüm Çelik, Asgar Jamneshan,
Guido Montúfar and Lorenzo Venturello), 20pp, submitted to
Journal of Symbolic Computation.
279.
Primary Ideals and their Differential Equations
(with Yairon CidRuiz and Roser Homs), 29pp, submitted
to Foundations of Computational Mathematics.
278.
DModules and Holonomic Functions
(with AnnaLaura Sattelberger), 36pp, presented at the
Math+ Fall School in Algebraic Geometry (FU Berlin, October 2019).
277.
Positivity Certificates via Integral Representations (with
Khazhgali Kozhasov and Mateusz Michalek), 22pp, submitted
to Fulton 80  LMS volume.
276. Theta Surfaces (with
Daniele Agostini, Türkü Özlüm Çelik and
Julia Struwe), 30pp, to appear in
Vietnam Journal of Mathematics;
Lecture slides.
275.
Discrete Statistical Models with Rational Maximum Likelihood Estimator
(with Eliana Duarte and Orlando Marigliano), 21pp,
to appear in Bernoulli.
274.
Algebraic Analysis of Rotation Data (with Michael Adamer, András
Lörincz and AnnaLaura Sattelberger), 21pp,
to appear in Algebraic Statistics.
273.
Estimating Linear Covariance Models with Numerical Nonlinear Algebra
(with Sascha Timme and Piotr Zwiernik), 23pp, to appear in
Algebraic Statistics.
272.
Voronoi Cells of Varieties (with
Diego Cifuentes, Kristian Ranestad and Madeleine Weinstein), 18pp,
to appear in
Journal of Symbolic Computation.
271.
Maximum Likelihood Estimation for Totally
Positive LogConcave Densities (with
Elina Robeva, Ngoc Tran and Caroline Uhler), 27pp,
to appear in Scandinavian Journal of Statistics.
270.
Brownian Motion Tree Models are Toric (with
Caroline Uhler and Piotr Zwiernik), 22pp,
to appear in Kybernetika.
269.
K3 Polytopes and their Quartic Surfaces (with
Gabriele Balletti and Marta Panizzut), 12pp,
to appear in Advances in Geometry.
268.
Moment Varieties of Measures on Polytopes (with
Kathlén Kohn and Boris Shapiro), 28pp,
to appear in Annali della Scuola Normale Superiore di Pisa.
267.
An Octanomial Model for Cubic Surfaces (with
Marta Panizzut and Emre Sertöz),
Le Matematiche 75 (2020) 517536.
266.
TwentySeven Questions about the Cubic Surface (with Kristian Ranestad),
Le Matematiche 75 (2020) 411424.
265.
The Schläfli Fan (with Michael Joswig and Marta Panizzut),
Discrete and Computational Geometry
64 (2020) 355381.
264.
The Geometry of SDPExactness in Quadratic Optimization
(with Diego Cifuentes and Corey Harris),
Mathematical Programming, Ser. A
182 (2020) 399428.
263. Optimal Transport to a Variety
(with Türkü Özlüm Çelik, Asgar Jamneshan,
Guido Montúfar and Lorenzo Venturello),
Mathematical Aspects of Computer and Information Sciences,
MACIS 2019, Istanbul, Springer Lecture Notes in Computer Science
11989 (2020) 364381.
262.
3264 Conics in a Second (with Paul Breiding and Sascha Timme),
Notices of the American Mathematical Society
67 (2020) 3037.
261.
Computing Convex Hulls of Trajectories (with Daniel Ciripoi,
Andreas Löhne and Nidhi Kaihnsa),
Revista de la Unión Matemática Argentina.
60 (2019) 637662.
260.
The Geometry of Gaussoids (with Alessio D'Ali,
Tobias Boege and Thomas Kahle),
Foundations of Computational Mathematics
19 (2019) 775812.
259. Schottky Algorithms: Classical Meets Tropical (with Lynn Chua and Mario Kummer), Mathematics of Computation
88 (2019) 25412558.
258.
Sixtyfour Curves of Degree Six
(with Nidhi Kaihnsa, Mario Kummer, Daniel Plaumann and Mahsa Sayyary),
Experimental Mathematics
28 (2019) 132150.
257. Learning Paths from Signature Tensors (with Max Pfeffer and Anna Seigal),
SIAM Journal on Matrix Analysis and Applications
40 (2019) 394416.
256.
Varieties of Signature Tensors (with
Carlos Améndola and Peter Friz),
Forum of Mathematics, Sigma
7 (2019) e10, 54 pp.
255.
Geometry of LogConcave Density Estimation
(with Elina Robeva and Caroline Uhler),
Discrete and Computational Geometry
61 (2019) 136160.
254.
Algebraic Identifiability of Gaussian Mixtures
(with Carlos Améndola and Kristian Ranestad),
International Mathematics Research Notices
21 (2018) 65566580.
253.
Learning Algebraic Varieties from Samples
(with Paul Breiding, Sara Kalisnik and Madeleine Weinstein),
Revista Matematica Complutense
31 (2018) 545593;
News story, Lecture.
252. Real Space Sextics and their Tritangents
(with Avinash Kulkarni, Yue Ren and Mahsa Sayyary),
Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2018),
ACM, New York, 2018, 247254.
251.
Distortion Varieties
(with Joe Kileel, Zuzana Kukelova and Tomas Pajdla),
Foundations of Computational Mathematics
18 (2018) 10431071.
250.
Nearest Points on Toric Varieties
(with Martin Helmer), Mathematica Scandinavica
122 (2018) 213238.
249. Changing Views on Curves
and Surfaces (with Kathlén Kohn and Matthew Trager),
Acta Mathematica Vietnamica
43 (2018) 129.
248.
Fitness, Apprenticeship, and Polynomials,
In: Combinatorial Algebraic Geometry,
(eds. G. Smith and B. Sturmfels), Fields Institute
Communications, Springer, New York, vol 80, (2017) 119.
247.
A Clever Elimination Strategy for Efficient Minimal Solvers
(with Joe Kileel, Zuzana Kukelova and Tomas Pajdla), 13pp,
IEEE Conference on Computer Vision and Pattern Recognition 2017
(CVPR 2017).
246. General
Models for Rational Cameras and the Case of TwoSlit Projections
(with Matthew Trager, John Canny, Martial Hebert and Jean Ponce), 9pp,
IEEE Conference on Computer Vision and Pattern Recognition 2017
(CVPR 2017).
245.
How to Flatten a Soccer Ball
(with Kaie Kubjas and Pablo Parrilo), In: Homological and
Computational Methods
in Commutative Algebra, (eds. A. Conca, J. Gubeladze and
T. Römer), Springer INdAM series, vol 20,
(2017) 141162
244.
Convexity in Tree Spaces (with Bo Lin, Xiaoxian Tang and Ruriko Yoshida),
SIAM Journal on Discrete Mathematics
31 (2017) 20152038.
243.
Real Rank Two Geometry
(with Anna Seigal), Journal of Algebra
484 (2017) 310333.
242.
Real Rank Geometry of Ternary Forms
(with Mateusz Michalek, Hyunsuk Moon and Emanuele Ventura),
Annali di Matematica Pura ed Applicata
196 (2017) 10251054.
241.
Congruences and Concurrent Lines in MultiView Geometry
(with Jean Ponce and Matthew Trager),
Advances in Applied Mathematics
88 (2017) 6291.
240.
Eigenconfigurations of Tensors (with Hirotachi Abo and Anna Seigal),
in Algebraic and Geometric Methods in
Discrete Mathematics, Contemporary Mathematics,
vol 685, American Mathematical Society,
(2017) 125.
239.
On the Existence of Epipolar Matrices
(with Sameer Agarwal, HonLeung Lee and Rekha Thomas),
International Journal of Computer Vision
121 (2017) 403415.
238.
Does Antibiotic Resistance Evolve in Hospitals?
(with Anna Seigal, Portia Mira and Miriam Barlow),
Bulletin of Mathematical Biology
79 (2017) 191208;
News story.
237.
The Hurwitz Form of a Projective Variety,
Journal of Symbolic Computation
79 (2017) 186196.
236.
Tropicalization of Del Pezzo surfaces
(with Qingchun Ren and Kristin Shaw),
Advances in Mathematics
300 (2016) 156189.
235. Tensors and their Eigenvectors,
Notices of the American Mathematical Society
63 (2016) 604606.
234. Symmetric Matrices, Catalan Paths, and Correlations (with Emmanuel Tsukerman and Lauren Williams),
Journal of Combinatorial Theory, Series A
144 (2016) 496510.
233. Rigid Multiview Varieties
(with Michael Joswig, Joe Kileel and André Wagner),
International Journal of Algebra and Computation
26 (2016) 775788.
232. Moment Varieties of Gaussian Mixtures
(with Carlos Améndola and JeanCharles Faugère),
Journal of Algebraic Statistics 7
(2016) 1428.
231.
Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental
(with Carlos Améndola and Mathias Drton),
Mathematical Aspects of Computer and Information Sciences,
(eds. I. Kotsireas, S. Rump and C. Yap),
MACIS 2015, Berlin, (2016) 579590.
230. Computing the Chow Variety of Quadratic Space Curves
(with Peter Bürgisser, Kathlén Kohn and Pierre Lairez),
Mathematical Aspects of Computer and Information Sciences,
(eds. I. Kotsireas, S. Rump and C. Yap),
MACIS 2015, Berlin, (2016) 130136.
229. Exponential Varieties
(with Mateusz Michalek, Caroline Uhler and Piotr Zwiernik),
Proceedings of the London Mathematical Society
112 (2016) 2756.
228.
The Euclidean distance degree of an algebraic variety (with Jan Draisma, Emil Horobet,
Giorgio Ottaviani, and Rekha Thomas),
Foundations of Computational Mathematics
16 (2016) 99149.
227.
Algebraic Systems Biology: a Case Study for the Wnt Pathway
(with Elizabeth Gross, Heather Harrington and Zvi Rosen),
Bulletin of Mathematical Biology
78 (2016) 2151.
226.
Decomposing Tensors into Frames
(with Luke Oeding and Elina Robeva),
Advances in Applied Mathematics
73 (2016) 125153.
225.
Duality of Multiple Root Loci (with Hwangrae Lee), Journal
of Algebra 446 (2016) 499526.
224.
CayleyBacharach Formulas
(with Qingchun Ren and Jurgen RichterGebert),
American Mathematical Monthly
122 (2015) 845854.
223.
Generic Spectrahedral Shadows (with Rainer Sinn),
SIAM Journal on Optimization
25 (2015) 12091220.
222.
Quartic spectrahedra
(with John Christian Ottem, Kristian Ranestad, and Cynthia Vinzant),
Mathematical Programming, Ser. B,
151 (2015) 585612.
221.
A Family of Quasisymmetry Models
(with Maria Kateri and Fatemeh Mohammadi),
Journal of Algebraic Statistics
6 (2015) 116.
220. Rational Design of Antibiotic Treatment Plans:
A Treatment Strategy for Managing Evolution and Reversing Resistance
(with Portia Mira, Kristina Crona, Devin Greene, Juan Meza and Miriam Barlow),
PLoS One
10(5) (2015) e0122283
219.
Tensors of nonnegative rank two
(with Elizabeth Allman, John Rhodes and Piotr Zwiernik),
Linear Algebra and its Applications
473 (2015) 3753.
218.
Moduli of Tropical Plane Curves
(with Sarah Brodsky, Ralph Morrison and Michael Joswig),
Research in the Mathematical Sciences
2:4 (2015)
217.
Fixed points of the EM algorithm and nonnegative rank boundaries
(with Kaie Kubjas and Elina Robeva),
Annals of Statistics
43 (2015) 422461.
216.
Exact solutions in structured lowrank approximation
(with PierreJean Spaenlehauer and Giorgio Ottaviani),
SIAM Journal on Matrix Analysis and Applications
35 (2014) 15211542.
215.
Hypersurfaces and their singularities in partial
correlation testing
(with Shaowei Lin, Caroline Uhler and Peter Bühlmann),
Foundations of Computational Mathematics
5 (2014) 10791116.
214.
Tropicalization of classical moduli spaces
(with Steven Sam and Qingchun Ren),
Mathematics in Computer Science
8 (2014) 119145.
213.
Maximum likelihood for matrices with rank constraints
(with Jonathan Hauenstein and Jose Rodriguez),
Journal of Algebraic Statistics
5 (2014) 1838.
212.
Likelihood geometry (with June Huh),
in Combinatorial Algebraic Geometry
(eds. Aldo Conca et al.),
Lecture Notes in Mathematics 2108,
Springer, (2014) 63117.
211.
The universal Kummer threefold
(with Gus Schrader, Steven Sam and Qingchun Ren),
Experimental Mathematics
22 (2013) 327362.
210.
A Hilbert scheme in computer vision
(with Chris Aholt and Rekha Thomas),
Canadian Journal of Mathematics
65 (2013) 961988.
209.
Mixed discriminants
(with Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein
and Sandra Di Rocco),
Mathematische Zeitschrift
274 (2013) 761778.
208.
Capacity prelog of noncoherent SIMO channels via Hironaka's theorem
(with V. Morgenshtern, E. Riegler, W. Yang, G. Durisi, S. Lin and
H. Bolcskei),
IEEE Transactions on Information Theory
59 (2013) 42134229.
207.
The entropic discriminant
(with Raman Sanyal and Cynthia Vinzant),
Advances in Mathematics
244 (2013) 678707.
206.
Elliptic curves in honeycomb form (with Melody Chan),
in "Tropical Geometry", Proceedings Castro Urdiales 2011,
editors E. Brugallé, M.A. Cueto, A. Dickenstein, E.M. Feichtner
and I. Itenberg, American Mathematical Society,
Contemporary Mathematics
589 (2013) 87107.
205.
Monomials, binomials, and RiemannRoch
(with Madhusudan Manjunath),
Journal of Algebraic Combinatorics
37 (2013) 737756.
204.
Toric cubes (with Alex Engström and Patricia Hersh),
Circolo Matematico di Palermo
62 (2013) 6778.
203.
Binary cumulant varieties (with Piotr Zwiernik),
Annals of Combinatorics
17 (2013) 229250.
202.
Combinatorial types of tropical eigenvectors (with Ngoc Tran),
Bulletin of the London Mathematical Society
45 (2013) 2736.
201.
Matrices with eigenvectors in a given subspace (with Giorgio Ottaviani),
Proceedings of the American Mathematical Society
141 (2013) 12191232.
200.
The number of eigenvalues of a tensor (with Dustin Cartwright),
Linear Algebra and its Applications
438 (2013) 942952.
199.
Geometry of higherorder Markov chains,
Journal of Algebraic Statistics
3 (2012) 110.
198.
Algebraic boundaries of Hilbert's SOS cones
(with Grigoriy Blekherman, Jonathan Hauenstein, John Christian Ottem
and Kristian Ranestad), Compositio Mathematica
148 (2012) 17171735.
197.
Graphical models for correlated defaults
(with I.O. Filiz, X. Guo and J. Morton),
Mathematical Finance
22 (2012) 621644.
196. Commutative algebra of statistical ranking (with Volkmar Welker),
Journal of Algebra
361 (2012) 264286.
195.
Computing linear matrix representations of HeltonVinnikov curves
(with Daniel Plaumann and Cynthia Vinzant),
in Mathematical Methods in Systems, Optimization and Control,
(eds. Harry Dym, Mauricio de Oliveira, Mihai Putinar),
Operator Theory: Advances and Applications", Vol 222, Birkhauser,
Basel, 2012, pp. 259277.
194. The central
curve in linear programming (with Jesus De Loera and Cynthia Vinzant),
Foundations of Computational Mathematics
12 (2012) 509540.
193.
On the convex hull of a space curve (with Kristian Ranestad),
Advances in Geometry 12 (2012) 157178.
192.
Mustafin varieties (with D. Cartwright, M. Haebich and A. Werner),
Selecta Mathematica
17 (2011) 757793.
191.
Noncoherent SIMO prelog via resolution of singularities
(with E. Riegler, V. Morgenshtern, G. Durisi, S. Lin and
H. Bolcskei), 6 pp.,
2011 IEEE International Symposium on Information Theory, St. Petersburg, Russia.
190.
Orbitopes (with R. Sanyal and F. Sottile),
Mathematika
57 (2011) 275314.
189.
The convex hull of a variety (with K. Ranestad),
in: "Notions of Positivity and the Geometry of Polynomials",
(eds. Petter Branden, Mikael Passare and Mihai Putinar),
Trends in Mathematics, Springer Verlag, Basel, 2011,
pp. 331344.
188.
Tropical quadrics through three points (with S. Brodsky),
Linear Algebra and its Applications
435 (2011) 17781785.
187.
Quartic curves and their bitangents (with D. Plaumann and
C. Vinzant), Journal of Symbolic Computation
46 (2011) 712733.
186.
Dualities in convex algebraic geometry (with P. Rostalski),
Rendiconti di Mathematica, Serie VII
30 (2010) 285327.
185.
Siphons in chemical reaction networks (with A. Shiu),
Bulletin of Mathematical Biology
72 (2010) 14481463.
184.
Geometry of the restricted Boltzmann machine (with M.A. Cueto
and J. Morton), in Algebraic Methods in Statistics and Probability,
(eds. M. Viana and H. Wynn), American Mathematical Society,
Contemporary Mathematics 516 (2010) 135153.
183.
Multivariate Gaussians, semidefinite matrix completion, and
convex algebraic geometry (with C. Uhler),
Annals of the Institute of Statistical Mathematics
62 (2010) 603638.
182.
Blowups of P^(n3) at n points and spinor varieties (with M. Velasco),
Journal of Commutative Algebra 2 (2010)
223244.
181.
The Hilbert scheme of the diagonal in a product of projective spaces (with D. Cartwright),
International Mathematics Research Notices
9 (2010) 17411771.
180.
Sagbi bases of CoxNagata rings (with Z. Xu),
Journal of the European Mathematical Society
12 (2010) 429459.
179.
Commuting birthdeath processes (with S. Evans and C. Uhler),
Annals of Applied Probability
20 (2010) 238266.
178. The algebraic degree of semidefinite programming (with J. Nie and K. Ranestad), Mathematical Programming
122 (2010) 379405.
177.
Polynomial relations among principal minors of a 4x4 matrix
(with S. Lin), Journal of Algebra
322 (2009) 41214131.
176.
Reconstructing spatiotemporal gene expression data from partial observations (with D. Cartwright, S. Brady, D. Orlando, and P. Benfey),
Bioinformatics
25 (2009) 25812587.
175.
Computer algebra in systems biology,
(with R. Laubenbacher), American Mathematical Monthly
116 (2009) 882891.
German version:
Computeralgebra in der Systembiologie,
InformatikSpektrum 32(1) (2009) 2732.
174.
Toric dynamical systems,
(with G. Craciun, A. Dickenstein and A. Shiu),
Journal of Symbolic Computation
44 (2009) 15511565.
173.
Marginal likelihood integrals for mixtures of independence models (with S. Lin and Z. Xu), Journal of Machine Learning Research
10 (2009) 16111631.
172.
Convex rank tests and semigraphoids (with
J. Morton, L. Pachter, A. Shiu and O. Wienand),
SIAM Journal on Discrete Mathematics
23 (2009) 11171134.
171.
Matrix cubes parametrized by eigenvalues (with J. Nie),
SIAM Journal on Matrix Analysis and Applications
31 (2009) 755766.
170.
Normal toric ideals of low codimension,
(with P. Dueck and S. Hosten),
Journal of Pure and Applied Algebra
213 (2009) 16361641.
169.
Tropical mathematics, (with D. Speyer), Mathematics Magazine
82 (2009) 163173.
168.
How to draw tropical planes (with S. Hermann, A. Jensen and M. Joswig),
Electronic Journal of Combinatorics
16(2) (2009) R6.
167. Comparison of pattern detection methods in microarray time series of the segmentation clock,
(with ML. Dequeant, 12 others, and O. Pourquie),
PLoS ONE 3(8) (2008) e2856.
166.
Elimination theory for tropical varieties (with J. Tevelev),
Mathematical Research Letters
15 (2008) 543562.
165.
Open problems in algebraic statistics, in
Emerging Applications of Algebraic Geometry,
(editors M. Putinar and S. Sullivant),
I.M.A. Volumes in Mathematics and its Applications,
149, Springer, New York, 2008, pp. 351364.
164.
The hyperdeterminant and triangulations of the 4cube,
(with P. Huggins, J. Yu and D. Yuster),
Mathematics of Computation
77 (2008) 16531679.
163.
Toric geometry of cuts and splits
(with S. Sullivant),
Michigan Mathematical Journal
57 (2008) 689709.
162.
Three counterexamples on semigraphoids
(with R. Hemmecke, J. Morton, A. Shiu and O. Wienand),
Combinatorics, Probability and Computing
17 (2008) 239257.
161.
Tropical implicitization and mixed fiber polytopes (with J. Yu)
in Software for Algebraic Geometry,
(editors M. Stillman, N. Takayama and J. Verschelde),
I.M.A. Volumes in Mathematics and its Applications
148, Springer, New York, 2008, pp. 111132.
160.
Semidefinite representation of the kellipse (with
J. Nie and P. Parrilo), in
Algorithms in Algebraic Geometry,
(editors A. Dickenstein, F. Schreyer and A. Sommese)
I.M.A. Volumes in Mathematics and its Applications,
146, Springer, New York, 2008, pp. 117132.
159.
Affine buildings and tropical convexity,
(with M. Joswig and J. Yu),
Albanian Journal of Mathematics
1 (2007) 187211.
158.
Conjunctive Bayesian networks
(with N. Beerenwinkel and N. Eriksson),
Bernoulli 13 (2007) 893909.
157.
Towards the human genotope (with P. Huggins and L. Pachter),
Bulletin of Mathematical Biology
69 (2007) 27232735.
156.
Epistasis and shapes of fitness landscapes,
(with N. Beerenwinkel and L. Pachter),
Statistica Sinica
17 (2007) 13171342.
155.
Hyperdeterminantal relations among symmetric principal minors,
(With O. Holtz), Journal of Algebra
316 (2007) 634648
154.
The cyclohedron test for finding periodic genes in time course
expression studies (with J. Morton, L. Pachter and A. Shiu),
Statistical Applications in Genetics and Molecular Biology
6 (2007) 1:21.
153. Tropical discriminants,
(with A. Dickenstein and E.M. Feichtner),
Journal of the American Mathematical Society
20 (2007) 11111133.
152. Analysis
of epistatic interactions and fitness
landscapes using a new geometric approach (with
N. Beerenwinkel, L. Pachter, S. Elena and R. Lenski),
BMC Evolutionary Biology 7:60 (2007)
151.
Computing the integer programming gap (with S. Hosten),
Combinatorica 27 (2007) 367382
150.
The Newton polytope of the implicit equation
(with J. Tevelev and J. Yu) Moscow Mathematical Journal
7 (2007) 327346.
149.
Algebraic factor analysis: tetrads, pentads and beyond,
(with M. Drton and S. Sullivant),
Probability Theory and Related Fields
138 (2007) 463493.
148.
The mathematics of phylogenomics (with L. Pachter),
SIAM Review 49 (2007) 331.
147.
Computing tropical varieties (with T. Bogart, A. Jensen,
D. Speyer and R. Thomas), Journal of Symbolic Computation
42 (2007) 5473.
146.
Monomial dynamical systems over finite fields
(with O. ColonReyes, A. Jarrah and R. Laubenbacher),
Complex Systems
16 (2006) 333342.
145.
Geometry of rank tests,
(with J. Morton, L. Pachter, A. Shiu and O. Wienand),
8 pp., Proceedings of the conference
Probabilistic Graphical Models (PGM 3),
Prague, Czech Republic, September 2006.
144.
Evolution on distributive lattices,
(with N. Beerenwinkel and N. Eriksson),
Journal of Theoretical Biology
242 (2006) 409420.
143.
An algebraic geometry approach to nonlinear parametric optimization in
control (with I. Fotiou, P. Rostalski and M. Morari),
American Control Conference,
Minneapolis, MN, June 2006, pp. 36183623.
142.
The maximum likelihood degree,
(with F. Catanese, S. Hosten and A. Khetan),
American Journal of Mathematics
128 (2006) 671697.
141.
Combinatorial secant varieties (with S. Sullivant),
Quarterly Journal of Pure and Applied Mathematics
2 (2006) 867891,
(Special issue: In Honor of Robert MacPherson).
140.
Minimizing polynomials via sum of squares over the gradient ideal
(with J. Demmel and J. Nie),
Mathematical Programming
106 (2006) 587606.
139.
Parametric alignment of Drosophila genomes,
(with C. Dewey, P. Huggins, K. Woods and L. Pachter),
PLOS Computational Biology,
2(6) (2006) e73.
138.
On the toric algebra of graphical models (with D. Geiger and C. Meek),
Annals of Statistics
34 (2006) 14631492
137.
Resultants in genetic linkage analysis (with I. Hallgrimsdottir),
Journal of Symbolic Computation 41
(2006) 125137
136.
Can biology lead to new theorems?
Clay Mathematics Institute Annual Report 2005,
Feature Article, pages 13, 2226.
135.
Matroid polytopes, nested sets and Bergman fans,
(with E.M. Feichtner),
Portugaliae Mathematica
62 (2005) 437468.
134.
What is a Grobner basis?,
Notices of the American Mathematical Society
52
(2005) 11991200
133.
Phylogenetic algebraic geometry,
(with N. Eriksson, K. Ranestad and S. Sullivant),
in Projective Varieties
with Unexpected Properties, (editors C. Ciliberto,
A. Geramita, B. Harbourne, RM. Roig and K. Ranestad),
De Gruyter, Berlin, 2005, pp. 237255
132.
Solving the likelihood equations,
(with S. Hosten and A. Khetan),
Foundations of Computational Mathematics.
5 (2005) 389407.
131.
On the tropical rank of a matrix (with F. Santos and M. Develin),
in Discrete and Computational Geometry, (eds. J.E. Goodman,
J. Pach and E. Welzl), Mathematical Sciences Research
Institute Publications, Volume 52, Cambridge University Press, 2005,
pp. 213242.
130.
The graph of monomial ideals (with K. Altmann),
Journal of Pure and Applied Algebra
201 (2005) 250263.
129.
First steps in tropical geometry (with J. RichterGebert and
T. Theobald), in
"Idempotent Mathematics and Mathematical Physics",
Proceedings Vienna 2003, (editors G.L. Litvinov and V.P. Maslov),
American Mathematical Society,
Contemporary Mathematics
377 (2005) 289317.
128.
Toric ideals of phylogenetic invariants, (with S. Sullivant),
Journal of Computational Biology
12 (2005) 204228.
127.
Algebraic geometry of Bayesian networks
(with L. Garcia and M. Stillman),
Journal of Symbolic Computation
39 (2005) 331355.
126.
Parametric inference for biological sequence analysis
(with L. Pachter),
Proceedings of the National Academy of Sciences
101 (2004) 1613816143.
125.
Tropical geometry of statistical models
(with L. Pachter),
Proceedings of the National Academy of Sciences
101 (2004) 1613216137.
124.
Algebraic recipes for integer programming,
"Trends in optimization" (Phoenix, AZ, 2004),
99113, Proc. Sympos. Appl. Math, 61,
Amer. Math. Soc., Providence, RI, 2004.
123.
Short rational functions for toric algebra (with J. A. De Loera,
D. Haws, R. Hemmecke, P. Huggins, and R. Yoshida),
Journal of Symbolic Computation
38 (2004) 959973.
122.
The tropical Grassmannian (with D. Speyer),
Advances in Geometry 4
(2004) 389411.
121.
Classification of sixpoint metrics
(with J. Yu), Electronic Journal of Combinatorics
11 (2004/05) R44.
120.
Multigraded Hilbert schemes (with M. Haiman),
Journal of Algebraic Geometry 13
(2004) 725769.
119. Supernormal
vector configurations (with S. Hosten and
D. Maclagan), Journal of Algebraic Combinatorics
19 (2004) 297313.
118. Tropical Convexity (with M. Develin), Documenta
Mathematica 9 (2004) 127.
117. Algebraic unimodular counting (with J. De
Loera), Mathematical Programming, Series B,
96 (2003) 183203.
116. Minimizing polynomial functions (with P.
Parrilo), Proceedings of the DIMACS Workshop on
Algorithmic and Quantitative Aspects of Real Algebraic
Geometry in Mathematics and Computer Science (March
2001), (eds. S. Basu and L. GonzalezVega), American
Mathematical Society, 2003, pp. 83100.
115. Higher Lawrence Configurations (with F. Santos),
Journal of Combinatorial Theory, Series A,
103 (2003) 151164.
114. Alexander duality in subdivisions of Lawrence
polytopes (with F. Santos), Advances in Geometry,
3 (2003) 177189.
113. Algorithms for the toric Hilbert scheme
(with M. Stillman and R. Thomas), in
Computations in Algebraic Geometry with Macaulay 2,
Algorithms Comput. Math., 8, Springer, Berlin, 2002, pp. 179214.
112. Ideals, varieties and Macaulay 2, in
Computations in Algebraic Geometry with Macaulay 2,
Algorithms Comput. Math., 8, Springer, Berlin, 2002, pp. 315.
111. Toric hyperkahler varieties (with T. Hausel),
Documenta Mathematica 7
(2002) 495534.
110. Elimination theory in codimension two (with
A. Dickenstein), Journal of Symbolic Computation
34 (2002) 119135.
109. Binomial residues (with E. Cattani and
A. Dickenstein), Annales de l'Institute Fourier
(Grenoble), 52 (2002), no. 3,
687708.
108.Syzygies of oriented matroids (with I. Novik
and A. Postnikov), Duke Mathematical Journal
111 (2002) 287317.
107.Grobner bases of abelian matrix groups, in
Symbolic Computation: Solving Equations in Algebra,
Geometry, and Engineering, (eds. E. Green, S.
Hosten, R. Laubenbacher, V. Powers), Contemporary
Mathematics, Volume 286, American Math. Soc, Providence,
RI, 2001, pp. 141143.
106.Rational hypergeometric functions (with
E. Cattani and A. Dickenstein), Compositio
Mathematica 128 (2001) 217240.
105. Syzygies of unimodular Lawrence ideals,
(with D. Bayer and S. Popescu), Journal fur
die Reine und Angewandte Mathematik 534
(2001) 169186.
104. A
sagbi basis for the quantum Grassmannian,
(with F. Sottile), Journal for Pure and Applied
Algebra 158 (2001) 347366.
103. Four counterexamples in combinatorial algebraic
geometry, Journal of Algebra 230
(2000) 282294.
102. Generic and cogeneric monomial ideals (with
E. Miller and K. Yanagawa), Journal of Symbolic
Computation 28 (2000) 691708.
101. Solving algebraic equations in terms of
${\cal A$hypergeometric series, Discrete
Mathematics 210 (2000) 171181.
100. Monomial ideals and planar graphs (with
E. Miller), in "Applied Algebra, Algebraic
Algorithms and ErrorCorrecting Codes", [M.
Fossorier, H. Imai, S. Lin and A. Poli, eds.],
Proceedings of AAECC13 (Honolulu, November 1999),
Springer Lecture Notes in Computer Science 1719
(1999) 1928.
99. Cutting corners (with S. Onn), Advances
in Applied Mathematics 23
(1999) 2948.
98. The CoScarf resolution, in "Commutative
Algebra, Algebraic Geometry and Computational
Methods", Proceedings Hanoi 1996, [editor
D. Eisenbud] Springer Verlag, Singapore, 1999,
pp. 315320.
97. Hypergeometric polynomials and integer programming
(with M. Saito and N. Takayama), Compositio
Mathematica 115 (1999) 185204.
96. Numerical Schubert calculus (with B. Huber
and F. Sottile), Journal of Symbolic Computation
20 (1998) 767788.
95. Syzygies of codimension $2$ lattice ideals,
(with I. Peeva), Mathematische Zeitschrift
229 (1998) 163194.
94. Cellular resolution of monomial modules (with
D. Bayer), Journal fur die Reine und Angewandte
Mathematik 502 (1998) 123140.
93. Grobner deformations of regular holonomic
systems (with M. Saito and N.Takayama), Proceedings
of the Japan Academy, Ser. A Math. Sci. 74
(1998) 111113.
92. Polynomial equations and convex polytopes,
American Mathematical Monthly 105
(1998) 907922.
91. Monomial resolutions (with D. Bayer and
I. Peeva), Mathematical Research Letters
5 (1998) 3146.
90. Residues and resultants (with E. Cattani
and A. Dickenstein), Journal of Mathematical
Sciences of the University of Tokyo 5
(1998) 119148.
89. Lattice walks and primary decomposition (with
P. Diaconis and D. Eisenbud), Mathematical Essays
in Honor of GianCarlo Rota, eds. B. Sagan and
R. Stanley, Progress in Mathematics, Vol. 161,
Birkhauser, Boston, 1998, pp. 173193.
88. Algebraic algorithms for sampling from conditional
distributions (with P. Diaconis), Annals
of Statistics 26 (1998)
363397.
87. Generic lattice ideals (with I. Peeva),
Journal of the American Mathematical Society
11 (1998) 363373.
86. Noncommutative Grobner bases for commutative
algebras (with D. Eisenbud and I. Peeva), Proceedings
of the American Mathematical Society 126
(1998) 687691.
85. How to shell a monoid (with I. Peeva and
V. Reiner), Mathematische Annalen 310
(1998) 379393.
84. Grobner bases and hypergeometric functions,
(with N. Takayama), in Grobner Bases and Applications
(Proc. of the Conference 33 Years of Grobner Bases),
B. Buchberger and F. Winkler (eds.), Cambridge
University Press, London Mathematical Society
Lecture Notes Series, 251, (1998), pp. 246258.
83. A toric ring with irrational PoincareBetti
series (with J.E. Roos), Comptes Rendus
Acad. Sci. Paris, Ser. I Math. 326
(1998) 141146.
82. Equations defining toric varieties, Algebraic
Geometry  Santa Cruz 1995, Proc. Sympos. Pure
Math., 62, Part 2, Amer. Math. Soc., Providence,
RI, 1997, pp. 437449.
81. Introduction to resultants, in: D. Cox, B.
Sturmfels (eds.), Applications of Computational
Algebraic Geometry, Proceedings of Symp. in Applied
Math., 53, American Mathematical Society, 1997,
pp. 2539.
80. Variation of cost functions in integer programming,
(with R.R. Thomas), Mathematical Programming
77 (1997) 357387.
79. Computing Hopf bifurcations (with J. Guckenheimer,
M. Myers), SIAM J. Numerical Analysis
34 (1997) 121.
78. Structural Grobner basis detection (with
M. Wiegelmann), Applicable Algebra in Engineering,
Communication and Computing (AAECC Journal) 8
(1997) 257263.
77. Bernstein's Theorem in affine space (with
B. Huber), Discrete and Computational Geometry
17 (1997) 137141.
76. Intersection theory on toric varieties (with
W. Fulton), Topology 36
(1997) 335353.
75. A normal form algorithm for modules over $k[x,y]/\langle
x y \rangle$ (with R. Laubenbacher), Journal
of Algebra 184 (1996) 10011024.
74. Binomial ideals (with D. Eisenbud), Duke
Mathematical Journal 84
(1996) 145.
73.
Mixed monomial bases (with P. Pedersen),
in Algorithms in Algebraic Geometry and Applications,
(eds. L. GonzalezVega and T. Recio), Progress
in Mathematics, Vol. 143, Birkhauser, Basel, 1996,
pp. 307316.
72. Computing multidimensional residues (with
E. Cattani, A. Dickenstein), in Algorithms in
Algebraic Geometry and Applications, (eds. L.
GonzalezVega and T. Recio), Progress in Mathematics,
Vol. 143, Birkhauser, Basel, 1996, pp. 135164.
71. Primitive partition identities (with P. Diaconis,
R. Graham), in Combinatorics, Paul Erdos is Eighty,
(eds. D.Mikl\'os, V.T. S\'os, T. Szonyi), Janos
Bolyai Mathematical Society, Budapest, Hungary,
1996, pp. 173192.
70. The polytope of all triangulations of a point
configuration (with J. De Loera, F. Santos, S.
Hosten), Documenta Mathematica 1
(1996) 103119.
69. Initial complexes of prime ideals (with M.
Kalkbrener) Advances in Mathematics 116
(1995) 365376.
68. On vector partition functions, J. of Combinatorial
Theory, Ser. A 72 (1995)
302309.
67. Grobner bases and triangulations of the second
hypersimplex (with J. De Loera, R. Thomas), Combinatorica
15 (1995) 409424.
66. A polyhedral method for solving sparse polynomial
systems (with B. Huber), Mathematics of Computation
64 (1995) 15411555.
65. Grobner bases of lattices, corner polyhedra,
and integer programming (with R. Weismantel,
G. Ziegler), Beitrage zur Algebra und Geometrie
36 (1995), 281298.
64. GRIN: An implementation of Grobner bases for
integer programming (with S.Hosten), in ``Integer
Programming and Combinatorial Optimization'',
[E. Balas and J. Clausen, eds.], Proceedings of
the IV. IPCO Conference (Copenhagen, May 1995),
Springer Lecture Notes in Computer Science 920
(1995) 267276.
63. Bounds for degrees of projective schemes,
(with N.V. Trung, W. Vogel), Mathematische
Annalen 302 (1995) 417432.
62. Introduction
to Chow forms (with J. Dalbec),
in "Invariant Methods in Discrete and Computational
Geometry" [N. White, ed.], Proceedings Curacao
(June 1994), Kluwer Academic Publishers, 1995,
pp. 3758.
61. Intersection
theory on spherical varieties (with W. Fulton,
R. MacPherson, F. Sottile), Journal of Algebraic
Geometry 4 (1995) 181193.
60. Viro's theorem for complete intersections,
Annali della Scuola Normale Superiore di Pisa.
(4) 21 (1994), no. 3, 377386.
59. On the number of real roots of a sparse polynomial, in Hamiltonian and Gradient Flows: Algorithms
and Control, (ed. A. Bloch), Fields Institute
Communications Vol. 3, American Math. Soc, Providence,
RI, 1994, pp. 137143.
58. Iterated fibre polytopes (with L.J. Billera),
Mathematika 41 (1994)
549555.
57. Cellular strings on polytopes (with L. Billera,
M. Kapranov), Proceedings of the Amer. Math.
Soc. 122 (1994) 549555.
56. A note on lattice simplices and toric varieties,
(with S. Onn), American Journal of Mathematics
116 (1994) 13371339.
55. Minimal polynomials and sparse resultants,
(with J. Yu), in "ZeroDimensional Schemes",
(eds. F. Orecchia and L. Chiantini), Proceedings
Ravello (June 1992), De Gruyter, Berlin, 1994,
pp. 317324.
54. A quantitative Steinitz Theorem (with S.
Onn), Beitrage zur Algebra und Geometrie
35 (1994) 125129.
53. Finding sparse systems of parameters (with
D. Eisenbud), Journal of Pure and Applied
Algebra 94 (1994) 143157.
52. On the Newton polytope of the resultant, Journal
of Algebraic Combinatorics 3
(1994) 207236.
51. Multigraded resultants of Sylvester type,
(with A. Zelevinsky), Journal of Algebra
163 (1994) 115127.
50. A note on polynomial reduction (with A. Reeves),
Journal of Symbolic Computation 11
(1993) 273277.
49. Product formulas for resultants and Chow forms,
(with P. Pedersen), Mathematische Zeitschrift
214 (1993) 377396.
48. Sparse elimination theory,
in "Computational
Algebraic Geometry and Commutative Algebra"
[D. Eisenbud and L. Robbiano, eds.], Proceedings
Cortona (June 1991), Cambridge University Press,
1993, pp. 264298.
47. Nonextremal Camion bases (with R.G. Bland,
C.W. Ko), Linear Algebra and its Applications
187 (1993) 195199.
46. Extension spaces of oriented matroids (with
G. Ziegler), Discrete and Computational Geometry
10 (1993) 2345.
45. Minkowski addition of polytopes: Computational
complexity and applications to Grobner bases,
(with P. Gritzmann), SIAM J. Discrete Math.
6 (1993) 246269.
44. Duality and minors of secondary polyhedra,
(with L.J. Billera, I.M. Gel'fand), Journal
of Combinatorial Theory B 57
(1993) 258268.
43. Maximal minors and their leading terms (with
A. Zelevinsky), Advances in Mathematics
98 (1993) 65112.
42. Asymptotic analysis of toric ideals, Memoirs
of the Faculty of Sciences, Kyushu University,
Series A: Mathematics 46, No. 2, (1992) 217228.
41. Chow polytopes and general resultants (with
M. Kapranov, A. Zelevinsky), Duke Mathematical
Journal 67 (1992) 189218.
40. Algorithms for the QuillenSuslin theorem,
(with A. Logar), Journal of Algebra
145 (1992) 231239.
39. Fiber polytopes (with L.J. Billera), Annals
of Mathematics 135 (1992)
527549.
38. Unimodular fans, toric manifolds and linear
codes (with P. Kleinschmidt and N. Schwartz),
in "Discrete and Computational Geometry:
Papers from the DIMACS Special Year", (eds.
J.E. Goodman, R. Pollack, W.L. Steiger), American
Math. Soc.. Providence, 1991, pp. 179186.
37. Computing combinatorial decompositions of
rings (with N. White), Combinatorica
11 (1991), 275293.
36. Quotients of toric varieties (with M. Kapranov,
A. Zelevinsky), Mathematische Annalen
290 (1991), 643655.
35. Computational algebraic geometry of projective
configurations, J. Symbolic Computation
11 (1991) 595618.
34. On the synthetic factorization of projectively
invariant polynomials (with W. Whiteley), J.
Symbolic Computation 11
(1991) 439454.
33. Grobner bases of toric varieties, Tohoku
Mathematical Journal 43
(1991) 249261.
32. On the topology and geometric construction
of oriented matroids and convex polytopes (with
J.Richter), Transactions American Math. Soc.
325 (1991) 389412.
31. Smooth toric varieties with small Picard number
are projective (with P. Kleinschmidt), Topology
30 (1991) 289299.
30. Stanley decompositions of the bracket ring,
(with N. White), Math. Scandinavica 67
(1990) 183189.
29. Constructions and complexity of secondary
polytopes (with L.J. Billera, P. Filliman), Advances
in Mathematics 83 (1990)
155179.
28. Grobner bases and Stanley decompositions of
determinantal rings, Mathematische Zeitschrift
205 (1990) 137144.
27. The intrinsic spread of a configuration in
$R^d$ (with J.E. Goodman, R. Pollack), Journal
American Math. Society 3
(1990) 639651.
26. All $11_3$ and $12_3$configurations are
rational (with N. White), Aequationes Mathematicae
39 (1990) 254260.
25. Nonrealizability proofs in computational geometry,
(with J. Bokowski, J. Richter), Discrete Comput.
Geometry 5 (1990) 333350.
24. Lawrence polytopes (with M. Bayer), Canadian
J. Mathematics 17 (1990)
6279.
23. On the existence of certain smooth toric varieties,
(with J. Gretenkort, P. Kleinschmidt), Discrete
Comput. Geometry 5 (1990)
255262.
22. Coordinate representation of order types requires
exponential storage (with J.E. Goodman, R. Pollack),
Proceedings of the 21st Annual ACM Symposium
on Theory of Computing, Seattle, 1989, pp.
405410.
21. Introduction to invariant theory in superalgebras,
(with GC. Rota), in D. Stanton (ed.): Invariant
Theory and Tableaux, I.M.A. Volumes in Mathematics
and its Applications, 19,
Springer, New York, 1989, pp. 135.
20. Proposal for a geometric algebra software
package (with T. Havel, N. White), SIGSAM
Bulletin 23 (1989) 1315.
19. Grobner bases and invariant theory (with
N. White), Advances in Mathematics 76
(1989) 245259.
18. On the matroid stratification of Grassmann
varieties, specialization of coordinates, and
a problem of N. White, Advances in Mathematics
75 (1989) 202211.
17. Computing final polynomials and final syzygies
using Buchberger's Grobner bases method, Resultate
der Mathematik 15 (1989)
351360.
16. An infinite family of minorminimal nonrealizable
$3$chirotopes (with J. Bokowski), Mathematische
Zeitschrift 200 (1989) 583589.
15. Arrangements of lines and pseudolines without
adjacent triangles (with D. Ljubic, J.P. Roudneff),
J. Combinatorial Theory A 50
(1989) 2432.
14. Uniform oriented matroids without the isotopy
property (with B. Jaggi, P. ManiLevitska, N.
White), Discrete Comput. Geometry 4
(1989) 97100.
13. Neighborly polytopes and oriented matroids,
European J. Combinatorics 9
(1988) 537546.
12. Tridiagonalization of complex matrices and
a problem of Longstaff, Linear Algebra Appl.
109 (1988) 165166.
11. Totally positive matrices and cyclic polytopes,
Linear Alg. Appl. 107
(1988) 275281.
10. Simplicial cells in arrangements and mutations
of oriented matroids (with J.P. Roudneff), Geometriae
Dedicata 27 (1988) 153170.
9. Some applications of affine Gale diagrams to
polytopes with few vertices, SIAM J. Discrete
Mathematics 1 (1988) 121133.
8. Aspects of computational synthetic geometry
 I. Algorithmic coordinatization of matroids,
in H. Crapo (ed.) : Computeraided geometric
reasoning, INRIA Rocquencourt, France, June
1987, pp. 5786.
7. Cyclic polytopes and $d$order curves, Geometriae
Dedicata 24 (1987) 103107.
6. Boundary complexes of convex polytopes cannot
be characterized locally, Journal London Math.
Soc. 35 (1987) 314326.
5. Polytopal and nonpolytopal spheres  An algorithmic
approach (with J. Bokowski), Israel Journal
of Mathematics 57 (1987)
257271.
4. On the decidability of diophantine problems
in combinatorial geometry, Bulletin American
Math. Soc. 17 (1987) 121124.
3. Reell realisierbare orientierte Matroide (with
J. Bokowski), in A. Kerber (ed.): "Diskrete
Strukturen, algebraische Methoden und Anwendungen",
Bayreuther Mathematische Schriften 21
(1986) 113.
2. Central and parallel projections of polytopes,
Discrete Mathem. 2 (1986)
315318.
1. On the coordinatization of oriented matroids,
(with J. Bokowski), Discrete and Computional
Geometry 1 (1986) 293306.
