Research Interests
My research is in commutative algebra and algebraic geometry, with a focus on minimal free resolutions, and their connections with representation theory and combinatorics. Specific topics of interest include finite group actions on free resolutions and the symbolic defect (follow the link for references on the subject). I am also interested in computational methods in commutative algebra and the development of mathematical software.
Publications
14. Jet Graphs (with E. Helmick and M. Walsh)
arXiv:2104.08933
13. The InvariantRing package for Macaulay2 (with L. Ferraro, F. Gandini, H. Huang, M. Mastroeni, and X. Ni)
arXiv:2010.15331
12. Betti numbers of symmetric shifted ideals (with J. Biermann, H. De Alba, S. Murai, U. Nagel, A. O'Keefe, T. Römer, and A. Seceleanu)
J. Algebra, 560:312--342, 2020 - arXiv:1907.04288
11. On the ideal generated by all squarefree monomials of a given degree
J. Commut. Algebra, 12(2):199--215, 06 2020 - arXiv:1609.06396
10. Betti numbers of toric ideals of graphs: A case study (with J. Hofscheier, G. Keiper, C. Kohne, M.E. Uribe-Paczka, and A. Van Tuyl)
J. Algebra Appl., 18(12):1950226, 14, 2019 - arXiv:1807.02154
9. The symbolic defect of an ideal (with A.V. Geramita, Y.S. Shin, and A. Van Tuyl)
J. Pure Appl. Algebra, 223(6):2709--2731, 2019 - arXiv:1610.00176
8. Degrees of regular sequences with a symmetric group action (with A.V. Geramita and D.L. Wehlau)
Canad. J. Math., 71(3):557--578, 2019 - arXiv:1610.06610
7. Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies (with H. Abe, L. DeDieu, and M. Harada) [the arXiv version contains corrections to the published version]
Selecta Math. (N.S.), 24(3):2129-2163, 2018 - arXiv:1612.08831
6. Symmetric complete intersections (with A.V. Geramita and D.L. Wehlau)
Comm. Algebra, 46:5, 2194-2204, 2018 - arXiv:1604.01101
5. Distinguishing \(\Bbbk\)-configurations (with Y.S. Shin and A. Van Tuyl)
Illinois J. Math., 61(3-4):415--441, 2017 - arXiv:1705.09195
4. Generators of truncated symmetric polynomials
J. Pure Appl. Algebra, 221(2):276-285, 2017 - arXiv:1011.6068
3. Propagating weights of tori along free resolutions
J. Symbolic Comput., 74:1-45, 2016 - arXiv:1406.1900
2. Free resolutions and modules with a semisimple Lie group action
J. Softw. Algebra Geom., 7(1):17-29, 2015
1. Computational Methods for Orbit Closures in a Representation with Finitely Many Orbits
Exp. Math., 23(3):310-321, 2014
Software
InvariantRing, computing invariants of group actions on polynomial rings in Macaulay2
BEMultipliers, Buchsbaum-Eisenbud multipliers package for Macaulay2
Points, ideals of points package for Macaulay2
HighestWeights, equivariant resolutions package for Macaulay2
Expository
Betti numbers with a dash of representations, CMS Notes 50, no. 1, 16, 2018
Select Talks
Jets of graphs
Department of Mathematics and Statistics Colloquium 2021, James Madison University
Symmetric shifted ideals
Combinatorial Algebra meets Algebraic Combinatorics 2020, Dalhousie University
The symbolic defect of an ideal
AMS Spring Central Sectional Meeting 2018, Ohio State University, Columbus
Distinguishing k-configurations
Mathematics Colloquium 2017, Dalhousie University
Towards Newton-Okounkov bodies of Hessenberg varieties
AMS Spring Western Sectional Meeting 2017, Washington State University, Pullman
Symmetric complete intersections
AMS Spring Southeastern Sectional Meeting 2016, University of Georgia, Athens
Equivariant resolutions of De Concini-Procesi ideals
Joint Mathematics Meetings 2015, San Antonio, TX
An algorithm for determining actions of semisimple Lie groups on free resolutions
Combinatorial Algebra meets Algebraic Combinatorics 2014, Dalhousie University
Free resolutions and representations with finitely many orbits
Algebraic Geometry Seminar 2013, Queen's University
Algorithms for irreducible decomposition of monomial ideals
Graduate Student Seminar 2012, Northeastern University
Risoluzioni libere di ideali determinantali
Welcome Home Workshop 2011, Università degli Studi di Torino
Generalized Tanisaki ideals and the cohomology of Hessenberg varieties
Graduate Student Seminar 2011, Northeastern University
Grassmannians and cluster algebras
Topics in representation theory 2009, Northeastern University
An introduction to Hodge algebras
Tapas Seminar 2009, Northeastern University
Ph.D. Dissertation
Free resolutions of orbit closures for representations with finitely many orbits
PDF - M2 files - arXiv:1210.6410