Research

My research is in commutative algebra, with a focus on its homological aspects. I have a particular interest in studying properties of commutative rings using theories of cohomological support and structures on resolutions, while drawing on ideas from a variety of other areas such as homotopy theory and representation theory. 

Below are preprints submitted for publication:

• • The embedded deformation problem for monomial ideals with Ben Briggs and Eloísa Grifo  (arXiv version)

Below are my published (or accepted) articles: 

(20) Resolutions of differential operators of low order for an isolated hypersurface singularity with Rachel Diethorn, Jack Jeffries, Claudia Miller, Nick Packauskas, Hamid Rahmati, and Sophia Vassiliadou, Michigan Mathematical Journal (2026): arXiv version

(19) High Frobenius pushforwards generate the bounded derived category with Matthew Ballard, Srikanth Iyengar, Patrick Lank, and Alapan Mukhopadhyay. Forum of Mathematics, Sigma (2026): arXiv version, journal version

(18) Classifying thick subcategories over a Koszul complex via the curved BGG correspondence with Jian Liu. Journal of the London Mathematical Society (2025): arXiv version, journal version 

(17) Lower bounds on Loewy lengths of modules of finite projective dimension with Nawaj KC, Advances in Mathematics (2025): arXiv version, journal version

(16) Koszul homomorphisms and universal resolutions in local algebra with Ben Briggs, James Cameron, and Janina Letz, Forum of Mathematics, Sigma (2025): arXiv version, journal version

(15) Relations on Poincaré series for quasi-complete intersection homomorphisms with Liana M Şega, Proceedings of the American Mathematical Society (2025): arXiv version, journal version

(14) Bounds on cohomological support varieties with Ben Briggs and Eloísa Grifo, Transactions of the American Mathematical Society, Series B (2024): arXiv version, journal version

(13) Cohomological jump loci and duality in local algebra with Ben Briggs and Daniel McCormick, Mathematische Zeitschrift (2023): arXiv version, journal version

(12) The homotopy Lie algebra of a Tor-independent tensor product with Luigi Ferraro, Mohsen Gheibi, Dave Jorgensen and Nicholas Packauskas, Illinois Journal of Mathematics (2023): arXiv version, journal version

(11) A comparison of dg algebra resolutions with prime residual characteristic with Michael DeBellevue, Quarterly Journal of Mathematics (2023): arXiv version, journal version

(10) A partial converse ghost lemma for the derived category of a commutative noetherian ring with Jian Liu, Proceedings of the American Mathematical Society (2023): arXiv version, journal version 

(9) Exceptional complete intersection maps of local rings with Srikanth Iyengar, Janina Letz, and Jian Liu, Pacific Journal of Mathematics (2022): arXiv version, journal version 

(8) Locally complete intersection maps and the proxy small property with Ben Briggs, Srikanth Iyengar, and Janina Letz, International Mathematics Research Notices IMRN (2022): arXiv version, journal version

(7) Constructing non-proxy small test modules for the complete intersection property with Ben Briggs and Eloísa Grifo, Nagoya Mathematical Journal (2022): arXiv version, journal version

(6) Cohomological supports of tensor products of modules over commutative rings with Srikanth Iyengar and William Sanders, Research in the Mathematical Sciences (2022): arXiv version, journal version 

(5) Support varieties over skew complete intersections via derived braided Hochschild cohomology with Luigi Ferraro and W. Frank Moore, Journal of Algebra (2022): arXiv version, journal version

(4) Cohomological supports over derived complete intersections and local rings, Mathematische Zeitschrift (2021): arXiv version, journal version

(3) Duality and symmetry of complexity over complete intersections via exterior homology with Jian Liu, Proceedings of the American Mathematical Society (2021): arXiv version, journal version

(2) Equivariant isomorphisms of Ext and Tor modules, Journal of Algebra (2020): arXiv version, journal version

(1) The derived category of a locally complete intersection ring, Advances in Mathematics (2019): arXiv version, journal version

 Below is my PhD thesis: (Advisors: Lucho Avramov and Mark Walker)

Thesis (2019), Digital Commons PDF

Software:

I am a coauthor of the ThickSubcategories package for Macaulay2 with Eloísa Grifo and Janina Letz. (Note: This is still under construction but available for use, click the first link.)