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)

  • Classifying thick subcategories over a Koszul complex via the curved BGG correspondence with Jian Liu (arXiv version)

  • High Frobenius pushforwards generate the bounded derived category with Matthew Ballard, Srikanth Iyengar, Patrick Lank, and Alapan Mukhopadhyay (arXiv version)

Below are my published articles: 

(18) 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 (to appear): arXiv 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.)