Branden Stone

Research

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.

Publications

  1. Recursive strategy for decomposing Betti tables of complete intersections.
    Joint with C. Gibbons and R. Huben.
    (Recently Submitted)
    [arXiv:1708.05440]

  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.
    [arXiv:1705.01139]

  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.
    [arXiv:1301.3441]

  4. A sequence defined by M-sequences.
    Discrete Math. 333 (2014), 35–38.
    Joint with Tom Enkosky.
    [arXiv:1308.4945]

  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.
    [arXiv:1307.6206]

  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.