Publications

  1. The F-regularity of algebraic sets related to commutator matrices (2024), Journal of Algebra. journal version
  2. Barile-Macchia resolutions with Selvi Kara (2024), Journal of Algebraic Combinatorics. journal version

Preprints

  1. Permanental ideals of symmetric matrices (2025). arXiv version
  2. Admissible matchings and the Castelnuovo-Mumford regularity of square-free powers with Kanoy Kumar Das, Amit Roy, and Kamalesh Saha (2025). arXiv version
  3. Homological invariants of edge ideals of weighted oriented graphs with Richie Sheng* and Debbie Wooton* (2025). arXiv version
  4. The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs with Nursel Erey and Aryaman Maithani (2025). arXiv version
  5. Edge ideals with linear quotients and without homological linear quotients with Kanoy Kumar Das and Aryaman Maithani (2025). arXiv version
  6. Realizing resolutions of powers of extremal ideals with Art M. Duval, Sara Faridi, Thiago Holleben, Susan Morey, and Liana M. Sega (2025). arXiv version
  7. Minimal cellular resolutions of monomial ideals with five generators and their Artinian reductions (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. Monomial ideals with minimal generalized Barile-Macchia resolutions with Huy Tai Ha and Aryaman Maithani (2024). arXiv version
  10. Minimal cellular resolutions of powers of graphs with Huy Tai Ha and Aryaman Maithani (2024). arXiv version
  11. Minimal cellular free resolutions of path ideals with Selvi Kara and Kyle Wang (2024). arXiv version
  12. 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 resolution. 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