Preprints

A new hierarchy of semidefinite programming relaxations for cycles in binary matroids and cuts in graphs , (with João Gouveia, Monique Laurent and Pablo Parrilo), arXiv:0907.4518

Theta bodies for polynomial ideals , (with João Gouveia and Pablo Parrilo), arXiv:0809.3480v2

Small Chvatal rank , (with Tristram Bogart), arXiv:0705.1027.

Articles in print

[1] An algebraic geometry algorithm for scheduling in presence of setups and correlated demands, (with Sridhar R. Tayur and N.R.Natraj), Mathematical Programming 69 (1995) 369-401.

[2] Groebner bases and triangulations of the second hypersimplex, (with Jesus de Loera and Bernd Sturmfels), Combinatorica 15 (1995) 409-424.

[3] A geometric Buchberger algorithm for integer programming, Mathematics of Operations Research 20 (1995) 864-884.

[4] Groebner bases in integer programming, (with Serkan Hosten), OPTIMA Mathematical Programming Society Newsletter 48 (1995).

[5] Test sets and inequalities for integer programs, (with Robert Weismantel) Proceedings of the 5th International IPCO conference, Vancouver , LNCS 1084 (1996) 16-30.

[6] Variation of cost functions in integer programming , (with Bernd Sturmfels), Mathematical Programming 77 (1997) 357-387.

[7] Truncated Groebner bases for integer programming, (with Robert Weismantel), Applicable Algebra in Engineering, Communication and Computing 8 (1997) 241-257.

[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 (1997) 119-142.

[9] Groebner bases in integer programming , Handbook of Combinatorial Optimization Vol. 1, D.-Z. Du and P.M.Pardalos eds., Kluwer Acad. Publ., Boston, MA (1998) 533-572.

[10] Groebner bases and integer programming, (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.

[11] The associated primes of initial ideals of lattice ideals , (with Serkan Hosten), Mathematical Research Letters 6 (1999) 83-97.

[12] Standard pairs and group relaxations in integer programming, (with Serkan Hosten), Journal of Pure and Applied Algebra 139 (1999) 133-157.

[13] Computing Groebner fans of toric ideals, (with Birk Huber), Experimental Mathematics 9 (2000) 321-331.

[14] Algebraic methods in integer programming , Encyclopedia of Optimization (eds: C. Floudas and P. Pardalos), Kluwer Academic Publishers, Dordrecht, 2001

[15] Combinatorics of the toric Hilbert scheme , (with Diane Maclagan), Discrete and Computational Geometry 27 (2002) 249-264.

[16] 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

[17] 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

[18] Gomory Integer Programs , (with Serkan Hosten), Mathematical Programming Series B 96 (2003) 271 - 292. math.OC/0106031.

[19] 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.

[20] Symmetric iterated Betti numbers , (with Eric Babson and Isabella Novik), Journal of Combinatorial Theory, Series A, 105 (2004) 233 - 254. math.CO/0206063.

[21] 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.

[22] 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.

[23] The structure of group relaxations, Discrete Optimization (eds: K. Aardal, G. Nemhauser, R. Weismantel), Handbooks in Operations Research and Management Science, Vol 12 , Elsevier, 2005.

[24] Reverse lexicographic and lexicographic shifting , (with Eric Babson and Isabella Novik), Journal of Algebraic Combinatorics, 23 (2006), no. 2, 107 - 123. math.CO/0507565.

[25] Moduli spaces of graded representations of finite dimensional algebras, (with Eric Babson and Birge Huisgen-Zimmermann), Contemporary Math., 419 (2006), 7--27.

[26] Computing tropical varieties , (with Tristram Bogart, Anders Jensen, David Speyer and Bernd Sturmfels), Journal of Symbolic Computation, 42 (2007), no. 1-2, 54--73.

[27] The generic Groebner walk , (with Komei Fukuda, Anders Jensen and Niels Lauritzen), Journal of Symbolic Computation, 43 (2007), no. 3, 298--312.

[28] The circuit ideal of a vector configuration , (with Tristram Bogart and Anders Jensen), Journal of Algebra, 309 (2007), no. 2, 518--542.

[29] Nice initial complexes of some classical ideals , (with Aldo Conca and Serkan Hosten), Contemporary Math., 423 (2007), 11--42.

[30] Computing Groebner fans , (with Komei Fukuda and Anders N. Jensen), Mathematics of Computation, 76 (2007), 2189--2212.

[31] 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.

[32] Moduli of McKay quiver representations II: Groebner basis techniques , (with Al\astair Craw and Diane Maclagan), Journal of Algebra, 316 (2007), no. 2, 514--535.