My doctoral dissertation dealt with the theory of maximal Cohen-Macaulay modules. In particular, I have been focused on determining if countable Cohen-Macaulay type implies finite Cohen-Macaulay type over a complete local Cohen-Macaulay ring with an isolated singularity. I am also interested in bounding projective dimension and various homological questions. Another area that I find very intriguing is the decomposition theory of Boij and Söderberg. I also enjoy working with Macaulay2. Below you will find a list of publications and maybe come current projects.


  1. Recursive strategy for decomposing Betti tables of complete intersections.
    Joint with C. Gibbons and R. Huben.
    (Recently Submitted)

  2. Generalized Multiplicative Indices of Polycyclic Aromatic Hydrocarbons and Benzeniod Systems.
    Zeitschrift für Naturforschung A, 72.6 (2017): 573-576.
    Joint with V.R. Kulli, Shaohui Wang, and Bing Wei.

  3. Non-simplicial decompositions of Betti diagrams of complete intersections.
    J. Commut. Algebra 7 (2015), no. 2, 189–206.
    Joint with Courtney Gibbons, Jack Jeffries, Sarah Mayes, Claudiu Raicu, and Brian White. Results from a summer workshop in commutative algebra at MSRI, 2011.

  4. A sequence defined by M-sequences.
    Discrete Math. 333 (2014), 35–38.
    Joint with Tom Enkosky.

  5. Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type.
    Connections between algebra, combinatorics, and geometry, 299–317, Springer Proc. Math. Stat., 76, Springer, New York, 2014.

  6. Super-stretched and graded countable Cohen-Macaulay type.
    Journal of Algebra 398C (2014), pp. 1-20.
    [Article], [arXiv:1301.3593]

  7. Computing free bases for projective modules
    The Journal of Software for Algebra and Geometry (2013).
    Joint with Brett Barwick.
    [Article] , [M2]

  8. Ideals with Larger Projective Dimension and Regularity.
    Journal of Symbolic Computation (2011).
    Joint with Jesse Beder, Jason McCullough, Luis Nunez, Alexandra Seceleanu, and Bart Snapp.
    [Article], [arXiv:1101.3368]

Macaulay 2 Packages

Research with Undergrads

At Bard all students are required to write a senior thesis for each concentration they choose. This includes the incarcerated students in the Bard Prison Initiative. For privacy reasons, I am not willing to publish the BPI students work. However, if you are interested in veiwing it, feel free to contact me. The titles of the current students are tentative.