The slack realization space of a polytope,
(with João Gouveia, Antonio Macchia and Amy Wiebe), August 2017.
Symmetry in Turán sums of squares polynomials from flag algebras,
(with Annie Raymond and Mohit Singh), July 2015.
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 An algebraic geometry
algorithm for scheduling in presence
of setups and correlated demands, (with Sridhar R. Tayur and
N.R.Natraj), Mathematical Programming 69
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triangulations of the second hypersimplex,
(with Jesus de Loera and Bernd Sturmfels), Combinatorica
15 (1995) 409-424.
 A geometric Buchberger
algorithm for integer programming,
Mathematics of Operations Research 20 (1995)
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(with Serkan Hosten),
OPTIMA Mathematical Programming Society Newsletter
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programs, (with Robert Weismantel)
Proceedings of the 5th International IPCO conference, Vancouver ,
LNCS 1084 (1996) 16-30.
 Variation of cost
functions in integer programming ,
(with Bernd Sturmfels), Mathematical Programming
 Truncated Groebner bases
for integer programming, (with Robert Weismantel), Applicable
Algebra in Engineering, Communication and Computing 8
 Applications to integer programming,
in Applications of Computational Algebraic Geometry,
D.A. Cox and B. Sturmfels eds.,
AMS Proceedings of Symposia in Applied Mathematics 53
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integer programming ,
Handbook of Combinatorial Optimization Vol. 1,
D.-Z. Du and P.M.Pardalos eds., Kluwer Acad. Publ.,
Boston, MA (1998) 533-572.
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(with Serkan Hosten), Groebner Bases and
Applications, B.Buchberger and F.Winkler eds.,
Cambridge University Press, London Math. Soc. Lecture Notes Series
251 (1998) 144-158.
 The associated primes
of initial ideals of lattice ideals , (with Serkan Hosten),
Mathematical Research Letters 6 (1999) 83-97.
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relaxations in integer programming, (with Serkan Hosten),
Journal of Pure and Applied Algebra 139
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fans of toric ideals, (with Birk Huber),
Experimental Mathematics 9 (2000)
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integer programming , Encyclopedia of
Optimization (eds: C. Floudas and P. Pardalos), Kluwer Academic
Publishers, Dordrecht, 2001
 Combinatorics of the toric Hilbert
scheme , (with Diane Maclagan), Discrete and Computational
Geometry 27 (2002) 249-264.
 Algorithms for the toric Hilbert
scheme , (with Mike Stillman and Bernd Sturmfels), a chapter in
Computations in Algebraic Geometry with Macaulay 2 (eds:
D. Eisenbud, D. Grayson, M. Stillman and B. Sturmfels), Algorithms and
Computation in Mathematics Vol 8, Springer 2002. pp 179-213
The Hilbert zonotope and a polynomial
time algorithm for universal Groebner bases , (with
Eric Babson and Shmuel Onn), Advances in Applied Math
30 (2003) 529-544. math.CO/0207135
 Gomory Integer Programs , (with
Serkan Hosten), Mathematical Programming Series B
96 (2003) 271 - 292.
The toric Hilbert scheme of a rank two lattice
is smooth and irreducible , (with Diane Maclagan),
Journal of Combinatorial Theory, Series A, 104 ,
Issue 1, (2003) 29--48. math.AG/0208031.
Symmetric iterated Betti numbers , (with Eric Babson and Isabella
Novik), Journal of Combinatorial Theory,
Series A, 105 (2004) 233 - 254.
 Creating weekly timetables for
maximizing employee preferences , (with Caleb Z. White, Youngbae
Lee, Yoonsoo Kim and Patrick Perkins), The UMAP Journal,
Vol. 25, No. 1. (2004) 5 - 24. More computational
tests can be seen in the older version
of the paper.
Toric initial ideals of $\Delta$-normal configurations:
Cohen-Macaulayness and degree bounds , (with Edwin O'Shea),
Journal of Algebraic Combinatorics, 21
(2005) 247 - 268. math.AC/0308109.
 The structure of group
Discrete Optimization (eds: K. Aardal, G. Nemhauser, R. Weismantel),
Handbooks in Operations Research and Management Science,
Vol 12 , Elsevier, 2005.
Reverse lexicographic and lexicographic shifting , (with Eric
Babson and Isabella Novik), Journal of Algebraic Combinatorics,
23 (2006), no. 2, 107 -
 Moduli spaces of graded representations of finite
dimensional algebras, (with Eric Babson and Birge Huisgen-Zimmermann),
Contemporary Math., 419 (2006), 7--27.
Computing tropical varieties , (with Tristram Bogart, Anders Jensen,
David Speyer and Bernd Sturmfels), Journal of Symbolic
Computation, 42 (2007), no. 1-2, 54--73.
The generic Groebner walk , (with Komei Fukuda, Anders Jensen and
Niels Lauritzen), Journal of Symbolic
Computation, 43 (2007), no. 3, 298--312.
The circuit ideal of a vector configuration , (with Tristram
Bogart and Anders Jensen), Journal of Algebra, 309
(2007), no. 2, 518--542.
 Nice initial
complexes of some classical ideals , (with Aldo Conca and Serkan
Hosten), Contemporary Math., 423
Computing Groebner fans , (with Komei Fukuda and Anders
N. Jensen), Mathematics of Computation,
76 (2007), 2189--2212.
Moduli of McKay quiver representations I: the coherent component ,
(with Alastair Craw and Diane Maclagan), Proceedings
of the London Math. Society (3), 95 (2007),
no. 1, 179--198.
Moduli of McKay quiver representations II: Groebner basis techniques
, (with Alastair Craw and Diane Maclagan),
Journal of Algebra, 316 (2007), no. 2,
Theta bodies for polynomial ideals , (with João Gouveia and Pablo Parrilo),
SIAM Journal of Optimization
Volume 20, Issue 4, (2010), 2097--2118.
Online Version at SIAM J. Opt.
Small Chvatal rank , (with Tristram Bogart and Annie Raymond),
Mathematical Programming, Series B Volume 124, Numbers 1-2, (2010)
Online version at Springer Link
 Convex Hulls of Algebraic Sets , (with João Gouveia), chapter in the "Handbook of Semidefinite, Cone and Polynomial Optimization", International Series in Operations Research & Management Science, Vol. 166, Miguel Anjos and Jean-Bernard Lasserre (eds), Springer, 2012.
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A new hierarchy of semidefinite programming relaxations for cycles in binary
matroids and cuts in graphs , (with João Gouveia, Monique Laurent
and Pablo Parrilo), Mathematical Programming, Series A 133 (2012), no. 1-2, 203--225.
A Hilbert scheme in computer vision, (with Chris Aholt and Bernd Sturmfels),
Canadian Journal of Mathematics 65 (2013), no. 5, 961-988
A QCQP Approach to Triangulation, (with Chris Aholt and Sameer Agarwal),
Computer Vision - ECCV 2012 ,
Lecture Notes in Computer Science 7572 (2012), 654-667.
Lifts of convex sets and cone factorizations, (with João Gouveia and Pablo Parrilo), Mathematics of Operations Research 38 (2013), 248-264.
Polytopes of minimum positive semidefinite rank,
(with João Gouveia and Richard Robinson),
Discrete & Computational Geometry Volume 50, Issue 3 (2013), 679-699.
Which nonnegative matrices are slack matrices?, (with João Gouveia,
Roland Grappe, Volker Kaibel, Kanstanstin Pashkovich and Richard Robinson),
Linear Algebra and its Applications 439 (2013) 2921-2933.
The Euclidean distance degree of an algebraic variety, (with
Jan Draisma, Emil Horobet, Giorgio Ottaviani and Bernd Sturmfels),
Foundations of Computational Mathematics 16:1 (2016) 99-149.
Approximate cone factorizations and lifts of polytopes, (with
João Gouveia and Pablo A. Parrilo),
Isaac Newton Institute preprint NI13069-POP,
Mathematical Programming, volume 151, Issue 2 (2015),
Worst-case results for positive semidefinite rank, (with
João Gouveia and Richard Robinson),
Mathematical Programming Series B , Volume 153, Issue 1 (2015) 201-212.
Positive semidefinite rank, (with
Hamza Fawzi, João Gouveia, Pablo A. Parrilo and Richard Z. Robinson),
Math Programming Series B , Volume 153, Issue 1 (2015) 133-177.
Counting real critical points of the distance to spectral matrix sets, (with
Dimitriy Drusvyatskiy and Hon-Leung Lee), SIAM J. Matrix Analysis and Applications , Volume 36, Issue 3 (2015), pp. 1360-1380.
Four dimensional polytopes of minimum positive semidefinite rank, (with
João Gouveia, Kanstanstin Pashkovich and Richard Z. Robinson),
J. Combin. Theory Ser. A 145 (2017), 184--226.
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The Euclidean distance degree of orthogonally invariant matrix varieties, (with
Dimitriy Drusvyatskiy, Hon-Leung Lee and Giorgio Ottaviani),
to appear in the
Israel Journal of Mathematics.
On the existence of epipolar matrices, (with
Sameer Agarwal, Hon-Leung Lee and Bernd Sturmfels),
Int. J. Comput. Vis. 121 (2017), no. 3, 403--415
Symmetric sums of squares over k-subset hypercubes
(with Annie Raymond, James Saunderson and Mohit Singh),
to appear in Mathematical Programming Series A.
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Certifying the existence of epipolar matrices, (with
Sameer Agarwal, Hon-Leung Lee and Bernd Sturmfels),