My research is in commutative algebra, and I am especially interested in its interactions with algebraic geometry and combinatorics. The goal of commutative algebra is to study commutative rings, and ideals and modules over them. An ideal in a polynomial ring can be interpreted as the vanishing locus of an algebraic variety, or can be associated with various combinatorial objects, such as a graph, a simplicial complex or a convex polytope. In this way, problems in commutative algebra, algebraic geometry and combinatorics are deeply interconnected with each other, and one can often solve problems in one of these areas by borrowing techniques from another one. Furthermore, one can sometimes use representation-theoretic methods to study the algebraic properties of ideals which are stable under permutation of the variables.
In this context, my work revolves around the study of Rees algebras of ideals and modules, with geometric motivations coming from the study of singularities, multiplicity theory, and toric algebraic geometry. Algebraically, I am interested in understanding integral dependence of ideals and modules, as well as in studying the asymptotic behavior of ordinary and symbolic powers of ideals for large exponents. Rees algebras have proved to be extremely useful tools for this, especially when considering ideals with a rich combinatorial structure.
(with Louiza Fouli, Kriti Goel, Kuei-Nuan Lin, Haydee Lindo, Whitney Liske and Maral Mostafazadehfard) Algebraic invariants of the special fiber ring of ladder determinantal modules, submitted, arXiv:2507.22167
(with Edward Price III and Matthew Weaver) On Rees algebras of ideals and modules with weak residual conditions, J. Algebra 690 (2026) 202-236, https://doi.org/10.1016/j.jalgebra.2025.10.043.
(with Edward Price III and Matthew Weaver) On Rees algebras of linearly presented ideals and modules, Collect. Math. 76, 455-475 (2025). https://doi.org/10.1007/s13348-024-00440-0
(with Alexandra Seceleanu) The combinatorial structure of symmetric strongly shifted ideals, J. Comb. Algebra 9 (2025), no. 3/4, pp. 209-263 doi: https://doi.org/10.4171/jca/107.
(with Kyle Maddox and Lance E. Miller) Rees algebras and generalized depth-like conditions in prime characteristic, Math. Nachr. (2023) 1-19, arXiv:2212.11374.
(with Louiza Fouli and Jooyoun Hong) Residual intersections and core of modules, J. Algebra 629 (2023), 227-246, arXiv:2205.13721
(with Ben Drabkin and Lorenzo Guerrieri) Rees algebras of ideals of star configurations, Linear Algebra and Appl. 645 (2022), 91-122, arXiv:2107.12260
(with Tan Dang) On the Cohen-Macaulay property of the Rees algebra of the module of differentials, Proc. Amer. Math. Soc. 150 (2022), 941-950, arXiv:2007.15772
Cohen-Macaulay fiber cones and defining ideal of Rees algebras of modules, Women in Commutative Algebra - Proceedings of the 2019 WICA Workshop, Association for Women in Mathematics Series, vol. 29, Springer (2022), arXiv:2011.08453
Residual intersections and modules with Cohen-Macaulay Rees algebras, J. Algebra 587 (2021), 36-63, arXiv:1811.08402
Rees algebras and fiber cones of modules doi.org/10.25394/PGS.9107936.v1