Publications

  1. Permanental ideals of symmetric matrices (2025), to appear in Proceedings of the American Mathematical Society. arXiv version
  2. Minimal cellular free resolutions of path ideals with Selvi Kara and Kyle Wang (2025), to appear in Electronic Journal of Combinatorics. arXiv version
  3. The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs with Nursel Erey and Aryaman Maithani (2025), Communications in Algebra. journal version
    4. . arXiv version
  4. Minimal cellular resolutions of monomial ideals with five generators and their Artinian reductions (2025), Journal of Pure and Applied Algebra. journal version. arXiv version
  5. Monomial ideals with minimal generalized Barile-Macchia resolutions, with Huy Tai Ha and Aryaman Maithani (2025), to appear in Vietnam Journal of Mathematics. arXiv version
  6. The F-regularity of algebraic sets related to commutator matrices (2024), Journal of Algebra. journal version. arXiv version
  7. Barile-Macchia resolutions, with Selvi Kara (2024), Journal of Algebraic Combinatorics. journal version. arXiv version

Preprints

  1. Periodicity of ideals of minors over some local rings and under deformation with Michale DeBellevue, Souvik Dey, K. Ganapathy, and Omkar Javadekar (2025). arXiv version
  2. Maximal minors of generic matrices have rational singularities with Manoj Kummini (2025). arXiv version
  3. Trees whose path ideals have linear quotients with Kanoy Kumar Das, Animikha Dutta Dhar, Pranath S Karanth, and Aniruda Suswaram (2025). arXiv version
  4. Admissible matchings and the Castelnuovo-Mumford regularity of square-free powers with Kanoy Kumar Das, Amit Roy, and Kamalesh Saha (2025). arXiv version
  5. Homological invariants of edge ideals of weighted oriented graphs with Richie Sheng* and Debbie Wooton* (2025). arXiv version
  6. Edge ideals with linear quotients and without homological linear quotients with Kanoy Kumar Das and Aryaman Maithani (2025). arXiv version
  7. Realizing resolutions of powers of extremal ideals with Art M. Duval, Sara Faridi, Thiago Holleben, Susan Morey, and Liana M. Sega (2025). arXiv version
  8. A family of simplicial resolutions which are DG-algebras with James Cameron, Sarasij Maitra, and Tim Tribone (2024). arXiv version
  9. Minimal cellular resolutions of powers of graphs with Huy Tai Ha and Aryaman Maithani (2024). arXiv version
  10. The MorseResolutions package for Macaulay2 with Selvi Kara and Augustine O'Keefe (2023). arXiv version

* denotes undergraduates.

I'd like to think of myself as a jack of all trades, and master of one. The only topic I can say I am an expert of is Barile-Macchia resolutions. Here are the broad topics I'm currently working on:

  • Constructing minimal free resolutions of monomial ideals
  • Persistence of associated primes of powers of monomial ideals
  • Computing regularity of powers of ideals
  • F-regularity/F-purity/F-injectivity
  • Golod rings
  • DG-algebras