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
| 20. | Jets and principal components of monomial ideals, and very well-covered graphs (with N. Iammarino and T. Yu) arXiv:2407.01836 |
| 19. | Experience in teaching quantum computing with hands-on programming labs (with H.H. López, M. Rahmati, J. Sang, and C. Yu) J. Supercomput., 80(10):14029--14056, 2024 |
| 18. | Betti numbers for connected sums of graded Gorenstein artinian algebras (with N. Altafi, R. Di Gennaro, S. Grate, R. M. Miro-Roig, U. Nagel, A. Seceleanu, and J. Watanabe) arXiv:2401.10492 |
| 17. | Setting the scene for Betti characters J. Softw. Algebra Geom., 13(1):45--51, 2023 - arXiv:2106.16062 |
| 16. | Computing with jets (with N. Iammarino) J. Softw. Algebra Geom., 12(1):43--49, 2022 - arXiv:2108.06350 |
| 15. | Jet Graphs (with E. Helmick and M. Walsh) Involve, 14(5):793--812, 2021 - arXiv:2104.08933 |
| 14. | Finite group characters on free resolutions J. Symbolic Comput., 113:29--38, 2022 - arXiv:2106.14071 |
| 13. | The InvariantRing package for Macaulay2 (with L. Ferraro, F. Gandini, H. Huang, M. Mastroeni, and X. Ni) J. Softw. Algebra Geom., 14(1):5--11, 2024 - 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
| Jets, compute jets of various algebraic, geometric and combinatorial objects in Macaulay2 |
| BettiCharacters, finite group characters on free resolutions and graded modules in Macaulay2 |
| 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
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Finite group actions on free resolutions AMS Spring Eastern Sectional Meeting 2022 (formerly at Tufts University) |
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Jets of graphs Department of Mathematics and Statistics Colloquium 2021, James Madison University |
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Symmetric shifted ideals Combinatorial Algebra meets Algebraic Combinatorics 2020, Dalhousie University |
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The symbolic defect of an ideal AMS Spring Central Sectional Meeting 2018, Ohio State University, Columbus |
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Distinguishing k-configurations Mathematics Colloquium 2017, Dalhousie University |
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Towards Newton-Okounkov bodies of Hessenberg varieties AMS Spring Western Sectional Meeting 2017, Washington State University, Pullman |
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Symmetric complete intersections AMS Spring Southeastern Sectional Meeting 2016, University of Georgia, Athens |
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Equivariant resolutions of De Concini-Procesi ideals Joint Mathematics Meetings 2015, San Antonio, TX |
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An algorithm for determining actions of semisimple Lie groups on free resolutions Combinatorial Algebra meets Algebraic Combinatorics 2014, Dalhousie University |
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Free resolutions and representations with finitely many orbits Algebraic Geometry Seminar 2013, Queen's University |
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Algorithms for irreducible decomposition of monomial ideals Graduate Student Seminar 2012, Northeastern University |
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Risoluzioni libere di ideali determinantali Welcome Home Workshop 2011, Università degli Studi di Torino |
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Generalized Tanisaki ideals and the cohomology of Hessenberg varieties Graduate Student Seminar 2011, Northeastern University |
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Grassmannians and cluster algebras Topics in representation theory 2009, Northeastern University |
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An introduction to Hodge algebras Tapas Seminar 2009, Northeastern University |
Ph.D. Dissertation
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Free resolutions of orbit closures for representations with finitely many orbits PDF - M2 files - arXiv:1210.6410 |