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. Calculations involving symbolic powers.
    The Journal of Software for Algebra and Geometry, Vol. 9 (2019), 71-80.
    Joint with B. Drabkin, E. Grifo, and A. Seceleanu.

  2. Recursive strategy for decomposing Betti tables of complete intersections.
    International Journal of Algebra and Computation, Vol. 29, No. 7 (2019).
    Joint with C. Gibbons and R. Huben.

  3. Advising undergraduate research in prison.
    Mathematical Outreach: Explorations in Social Justice Around the Globe, 255-263.
    Series on Mathematics Education: Vol 16, World Scientific, November 2019.

  4. Visualizing combinatorial objects in Macaulay2.
    Sém. Lothar. Combin. 80B (2018), Art. 97, 6 pp.
    Joint with B. Barwick, T. Enkosky, and J. Vallandingham.

  5. 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.

  6. 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.

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

  8. 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.

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

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

  11. 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.