Papers

  • Lattice complements and the subadditivity of syzygies of simplicial forests (pdf)
    Journal of Commutative Algebra, to appear.
  • Simplicial Complexes are Game Complexes (pdf)
    With Svenja Huntemann and Richard Nowakowski (May 2016).
  • Resolutions of monomial ideals of projective dimension 1, (pdf)
    With Ben Hersey,
    Communications in Algebra, vol. 45, no. 12, 5453–5464 (2017).
  • Betti numbers of monomial ideals via facet covers, (pdf)
    With Nursel Erey,
    Journal of Pure and Applied Algebra, Volume 220, Issue 5, Pages 1990-2000 (May 2016).
  • Multigraded Betti numbers of simplicial forests, (pdf)
    With Nursel Erey,
    Journal of Pure and Applied Algebra, Volume 218, Pages 1800 -- 1805 (04-March-2014).
  • The projective dimension of sequentially Cohen-Macaulay monomial ideals, (pdf)
    (October 2013).
  • Games and Complexes I: Transformation via Ideals, (pdf)
    With Svenja Huntemann and Richard Nowakowski,
    To appear in Games of Chance, no. 5, Cambridge University Press (2016).
  • Games and Complexes II: Weight Games and Kruskal-Katona Type Bounds, (pdf)
    With Svenja Huntemann and Richard Nowakowski,
    To appear in Games of Chance, no. 5, Cambridge University Press (2016).
  • When is a Squarefree Monomial Ideal of Linear Type?, (pdf)
    With Ali Alilooee,
    Commutative Algebra and Noncommutative Algebraic Geometry II, MSRI Publications, Volume 68, Cambridge University Press, Cambridge, (2015)
  • A criterion for a monomial ideal to have a linear resolution in characteristic 2, (pdf)
    With Emma Connon,
    Electronic Journal of Combinatorics, Volume 22, Issue 1 (2015).
  • A good leaf order on simplicial trees, (pdf)
    Connections Between Algebra, Combinatorics, and Geometry, Springer Proceedings in Mathematics & Statistics, Vol. 76 (May 2014).
  • The Betti numbers of Stanley-Reisner ideals of simplicial trees, (pdf)
    (February 2013).
  • Graded Betti numbers of the path ideals of cycles and lines, (pdf)
    With Ali Alilooee (January 2013).
  • Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution, (pdf)
    With Emma Connon,
    Journal of Combinatorial Theory, Series A 120, pp. 1714-1731 (2013).
  • Monomial resolutions supported by simplicial trees, (pdf)
    Journal of Commutative Algebra, Volume 6, Number 3 (Fall 2014).
  • On the resolution of path ideals of cycles, (pdf)
    With Ali Alilooee,
    Communications in Algebra, Volume 43, Issue 12, pages 5413-5433 (2015).
  • Odd-cycle-free complexes and the Koenig property, (ps pdf)
    With Massimo Caboara,
    Rocky Mountain Journal of Mathematics, Volume 41, Number 4, Pages 1059--1079 (2011).
  • The defining ideals of conjugacy classes of nilpotent matrices and a conjecture of Weyman,(pdf)
    With Riccardo Biagioli and Mercedes Rosas,
    International Mathematics Research Notices, Vol. 2008 : article ID rnn117 (Oct 2008).
  • The reconstruction conjecture on edge ideals, (ps)
    With Kia Dalili and Will Traves,
    Discrete Mathematics, Volume 308 Issue 10, Pages 2002--2010 (May 2008).
  • Simplicial cycles and the computation of simplicial trees, (ps)
    With Massimo Caboara and Peter Selinger,
    Journal of Symbolic Computation, Volume 42, Issues 1-2, Pages 74--88 (January-February 2007).
  • De Concini-Procesi ideals indexed by hooks, (dvi pdf)
    With Riccardo Biagioli and Mercedes Rosas .
    Communications in Algebra, Volume 35, Issue 12, pages 3875--3891 (November 2007).
  • Tree checking for sparse complexes,
    With Massimo Caboara and Peter Selinger,
    Springer Lecture Notes Series in Computer Science (LNCS), Volume 4151, 110--121 (2006).
  • Monomial ideals via square-free monomial ideals, (ps pdf)
    Lecture Notes in Pure and Applied Mathematics, volume 244, 85--114 (2005).
  • Cohen-Macaulay properties of square-free monomial ideals, (ps pdf)
    Journal of Combinatorial Theory, Series A, 109, no. 2, 299--329 (2005).
  • Simplicial trees are sequentially Cohen-Macaulay, (ps pdf)
    J. Pure and Applied Algebra, Volume 190, Issues 1-3, Pages 121-136 (June 2004).
  • The facet ideal of a simplicial complex, (ps pdf )
    Manuscripta Mathematica 109, 159--174 (2002).
  • Blowup closure with applications to TI closure, (dvi ps pdf)
    Journal of Algebra 249, 472--511 (2002).
  • Normal ideals of graded rings, (dvi ps pdf)
    Communications in Algebra, vol. 28, no.4, 1971--1977 (2000).




  • A class of normal ideals,
    Under repair.

    Other:

  • Computational Algebra and Combinatorics of Toric Ideals, (pdf)
    Authors: Diane Maclagan, Rekha R. Thomas, Sara Faridi, Leah Gold, A.V. Jayanthan, Amit Khetan, Tony Puthenpurackel.
    Lectures and tutorials from the 2003 workshop on Computational Algebra and Combinatorics at Harish Chandra Research Institute, Allahabad, India (I wrote Tutorial 4) (2005).

  • Local cohomology and the Cohen-Macaulay property, (pdf)
    With Florian Enescu. Lecture prepared for supplementary talk at Minnowbrook Workshop on Commutative Algebra, NY, August 2005.
  • Simplicial tree computations, (ps pdf)
    With Massimo Caboara and Peter Selinger , extended abstract for MEGA 2005 Conference.
  • Primary decomposition in a sequentially Cohen-Macaulay module, (dvi pdf)
    This is now inside the paper "Monomial ideals via square-free monomial ideals".
  • Closure operations on ideals, (dvi ps pdf)
    Thesis, University of Michigan, Ann Arbor, June 2000.
    Advisor: Karen E. Smith .

  • Simplicial trees: properties and applications, (pdf ps )
    An outline of the main results in facet ideal theory. This short note is the abstract of a talk I gave at the International Conference on Commutative Algebra & Combinatorics in Allahabad, India, December 2003.
  • Poster: Properties of simplicial trees, (Click here)
    Presented at the CoCoA Conference in Universidad de Cádiz (Spain) 2-7 June, 2003.
  • Poster: Closure operations on ideals, (Click here)
    Presented at the January 2000 AWM workshop in Washington DC.


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