Research Interests
My research is in commutative algebra and algebraic geometry. I am particularly interested in minimal free resolutions over polynomial rings, and connections with representation theory and combinatorics. I am also interested in computational methods in commutative algebra.
Publications
11. 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)
arXiv:1807.02154
10. Distinguishing \(\Bbbk\)-configurations (with Y.S. Shin and A. Van Tuyl)
arXiv:1705.09195
9. The symbolic defect of an ideal (with A.V. Geramita, Y.S. Shin, and A. Van Tuyl)
arXiv:1610.00176
8. On the ideal generated by all squarefree monomials of a given degree
arXiv:1609.06396
7. Geometry of Hessenberg varieties with applications to Newton-Okounkov bodies (with H. Abe, L. DeDieu, and M. Harada)
Selecta Math. (N.S.), 24(3):2129-2163, 2018 - arXiv:1612.08831
6. Degrees of regular sequences with a symmetric group action (with A.V. Geramita and D.L. Wehlau)
Canad. J. Math., 2018 - arXiv:1610.06610
5. Symmetric complete intersections (with A.V. Geramita and D.L. Wehlau)
Comm. Algebra, 46:5, 2194-2204, 2018 - arXiv:1604.01101
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
HighestWeights, package for Macaulay2
Points, package for Macaulay2
Expository
Betti numbers with a dash of representations, CMS Notes 50, no. 1, 16, 2018
Select Talks
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