Research
My doctoral dissertation dealt with the theory of maximal CohenMacaulay modules. In particular, I have been focused on determining if countable CohenMacaulay type implies finite CohenMacaulay type over a complete local CohenMacaulay 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

Recursive strategy for decomposing Betti tables of complete intersections.
Joint with C. Gibbons and R. Huben.
(Recently Submitted)
[arXiv:1708.05440] 
Generalized Multiplicative Indices of Polycyclic Aromatic Hydrocarbons and Benzeniod Systems.
Zeitschrift für Naturforschung A, 72.6 (2017): 573576.
Joint with V.R. Kulli, Shaohui Wang, and Bing Wei.
[arXiv:1705.01139] 
Nonsimplicial 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] 
A sequence defined by Msequences.
Discrete Math. 333 (2014), 35–38.
Joint with Tom Enkosky.
[arXiv:1308.4945] 
NonGorenstein isolated singularities of graded countable CohenMacaulay type.
Connections between algebra, combinatorics, and geometry, 299–317, Springer Proc. Math. Stat., 76, Springer, New York, 2014.
[arXiv:1307.6206] 
Superstretched and graded countable CohenMacaulay type.
Journal of Algebra 398C (2014), pp. 120.
[Article], [arXiv:1301.3593] 
Computing free bases for projective modules
The Journal of Software for Algebra and Geometry (2013).
Joint with Brett Barwick.
[Article] , [M2] 
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

Visualize.m2 (in development): Joint with Brett Barwick, Tom Enkosky, and Jim Vallandingham. This package helps visualize algebraic objects in the browser using javascript.

Decompositions.m2: Joint with Courtney Gibbons during the MSRI Summer School in Commutative Algebra. This is a patch to supplement to the current BoijSöderberg Macaulay2 package. This package allows the user to compute the coefficients of a Betti Table decomposition using the HerzogKohl equations and is included in the current version of the BoijSoederberg.m2 package in Macaulay2.

QuillenSuslin.m2 This is joint with Brett Barwick. Given a projective module over a polynomial ring, this package uses LogarSturmfels’ algorithm to calculate the free basis.

BigIdeal.m2 This package generates the ideals defined in Ideals with Larger Projective Dimension and Regularity by Beder, McCullough, Nunez, Seceleanu, Snapp and Stone. These ideals have very large projective dimension and regularity relative to the degree and number of generators.
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.
 Finding Complex Roots Current
 Nicholas DeMarco, Adelphi University

(Coadvised with Sarah Wright)
 Linear Programming with Macaulay2 Current

Kyle Murray, Adelphi University
 Walks on molecular graphs May 2017

Marisa Masi, Adelphi University
 Matroids on Rings with applications to toric ideals May 2017
 Patrick Phelps, Adelphi University
 From String Theory to Elliptic Curves over Finite Field, $\mathbb{F}_p$ May 2014

Linh Pham, Bard College
 Let’s Walk and Explore May 2014

Bard College (BPI)
 A New Look at Hadwiger’s Conjecture May 2014

Bard College (BPI)
 Concrete Bridges to Abstract Algebras May 2014

Bard College (BPI)
 Sifting Squared Prime Intervals Efficient Prime Acquisition and Counting May 2014

Bard College (BPI)
 Algebraic Structures and BoijSöderberg Theory May 2013

Fanny WyrickFlax, Bard College
 Applications of Graph Theory to Chaotic Systems January 2013
 Bard College (BPI)

(Coadvised with Georgi Gospodinov)
 Computing Various Dimensions of Chaotic Systems January 2013
 Bard College (BPI)
 (Coadvised with Georgi Gospodinov)