Books:

• Computational Algebra and Combinatorics of Toric Ideals.
      Lecture notes from the International Conference on Commutative Algebra and Combinatorics in PDF and Postscript.
      Ramanujan Mathematical Society Lecture Notes Series, Volume 4. ISBN: 978-81-902545-4-0.
• Tropical Geometry and Integrable Systems. Edited with Chris Athorne and Ian Strachan. Proceedings of the conference on tropical geometry and integrable systems, held July 3-8, 2011, at the University of Glasgow.
• Introduction to Tropical Geometry, with Bernd Sturmfels.

• Toric and tropical Bertini theorems in positive characteristic. With Francesca Gandini, Milena Hering, Fatemeh Mohammadi, Jenna Rajchgot, Ashley K. Wheeler, and Josephine Yu. arXiv:2111.13214.
• The spine of the T-graph of the Hilbert scheme of points in the plane. With Rob Silversmith. arXiv:2111.00819.
• Varieties of Tropical Ideals are Balanced. With Felipe Rincón. arXiv:2009.14557. To appear in Advances in Mathematics
• The Cox ring of \overline{M}_{0,6}. With Martha Bernal Guillén. arXiv:1712.081293.
• Computing Tropical Varieties in Macaulay2. With Carlos Améndola, Kathlén Kohn, Sara Lamboglia, Ben Smith, Jeff Sommars, Paolo Tripoli, and Magdalena Zajaczkowska. arXiv:1710.10651.

• Higher Connectivity of Tropicalizations. With Josephine Yu. arXiv:1908.05988 To appear in Math. Annal. DOI
• Tropical ideals (with Felipe Rincón). arXiv:1609.03838. Compositio Mathematica , Volume 154 , Issue 3 , March 2018 , pp. 640 - 670
• Tropical schemes, tropical cycles, and valuated matroids (with Felipe Rincón). arXiv:1401.4654. Journal of the European Mathematical Society, Volume 22, Issue 3, 2020, pp777-706
• Gröbner bases over fields with valuations. With Andrew Chan. arxiv.1303.0729. The accompanying Macaulay 2 package is available here. Math. Comp. 88 (2019), 467-483
• Polyhedral structures on tropical varieties. Mostly survey article for the Bellairs proceedings. arxiv.1302.5372. AMS Contemporary Mathematics Volume Tropical and Non-Archimedean Geometry
• Introduction to tropical algebraic geometry. Survey article. arxiv.1207.1925. AMS Contemporary Mathematics Volume "Tropical Geometry and Integrable Systems".
• The T-graph of a multigraded Hilbert scheme
      arXiv.1110.1861. With Milena Hering. Experimental Mathematics, 21, no 3, 280-297, 2012. The accompanying Macaulay 2 package is available here.
• Lower and upper bounds for nef cones.
      arXiv.1009.0220. With Angela Gibney. The accompanying Macaulay 2 package is available here. To appear in IMRN (doi: 10.1093/imrn/rnr121)
• Equations for Chow and Hilbert quotients.
      arXiv.0707.1801. With Angela Gibney. Journal of Algebra and Number Theory, 4 (2010), No 7, 855-885.
• Smooth and irreducible multigraded Hilbert schemes.
      Advances in Mathematics, 223 (2010) 1608-1631. arXiv.0811.3594. With Greg Smith.
• Some cases of the Eisenbud-Green-Harris conjecture.
      Math. Res. Lett. 15 (2008), no 3, 427--433. math.AC/0611488. With Giulio Caviglia.
• Fiber fans and toric quotients
      Discrete and Computational Geometry, 37, 251--266, 2007. math.AG/0510128. With Alastair Craw.
• Moduli of McKay quiver representations I: The coherent component.
      Proceedings of the LMS, 95, 179--198, 2007. math.AG/0505115. With Alastair Craw and Rekha R. Thomas.
• Moduli of McKay quiver representations II: Grobner basis techniques.
      Journal of Algebra, 316, 2, 515--535, 2007 (Computational Algebra section). math.AG/0611840.
      With Alastair Craw and Rekha R. Thomas.
• The card game Set.
      The Mathematical Intelligencer, 25, No. 3, 2003, 33-40. With Ben Davis.
• Multigraded Castelnuovo-Mumford Regularity..
      Journal für die reine und angewandte Mathematik (Crelle's Journal), 571, (2004), 179-212.. math.AC/0305214.
      With Greg Smith.
• Uniform Bounds on Multigraded Regularity.
      Journal of Algebraic Geometry, 14, no. 1, 2005, 137-164. math.AG/0305215. With Greg Smith.
• The toric Hilbert scheme of a rank two lattice is smooth and irreducible.
      Journal of Combinatorial Theory, Series A, 104, no.1, (2003), 29-48. math.AG/0208031. With Rekha Thomas .
• Supernormal Vector Configurations.
      Journal of Algebraic Combinatorics, 19, no. 3, (2004), 297-313. math.CO/0105036.
      With Serkan Hosten and Bernd Sturmfels .
• The Vertex Ideal of a Lattice.
      Advances in Applied Mathematics, 29, 2002, 521-538. math.CO/0012197. With Serkan Hosten .
• Combinatorics of the toric Hilbert scheme
      Discrete and Computational Geometry, 27, 2002, no. 2, 249-272. math.AG.9912014. With Rekha Thomas .
• Antichains of Monomial Ideals are Finite.
      Proceedings of the AMS, 129, 2001, no. 6, 1609-1615. math.CO.9909168.
• Boolean Term Orders and the Root System B_n.
      Order 15 (3):279-295, 1998. math.CO.9809134.
• Equivalent methods for global optimization.
      In State of the art in global optimization (Princeton, NJ, 1995), 201-211, Nonconvex Optim. Appl., 7,
      Kluwer Acad. Publ., Dordrecht, 1996. With Timothy Sturge and William Baritompa .

• Tropical.m2, a package to do tropical computations with Macaulay2. The accompanying short paper is available here. Written with: Carlos Améndola, Kathlén Kohn, Sara Lamboglia, Ben Smith, Jeff Sommars, Paolo Tripoli, and Magdalena Zajaczkowska.

• Notes on Hilbert schemes.
      Lecture notes from five lectures on Hilbert schemes given at the Summer School on
      Introduction to explicit methods in algebraic geometry, run September 3-7, 2007, at the University of Warwick.
• Lecture notes on tropical geometry
      from the AARMS Summer School at UNB in July/August 2008.
• Lecture notes on tropical geometry
      from the ELGA 2011 graduate school in Buenos Aires, August 2011.
  Videos of the lectures are available here.
• Lecture notes on Tropical Geometry from the LMS Undergraduate Summer School at the University of Manchester, July 2017.
• Multigraded Hilbert schemes. Notes from the school on Hilbert schemes, McKay correspondence, and singularities, Paris, 16--18 December, 2019.

• Structures on Sets of Monomial Ideals , submitted May 2000.

• The tropical inverse problem and cones of effective cycles.