My current projects all involve commutative algebra over the Cox ring of projective toric varieties. See my oral exam presentation for some topics and questions that I am currently working on.

Publications and preprints

• Bounds on Multigraded Regularity
  With Juliette Bruce, Lauren Cranton Heller
  arXiv:2208.11115 [math.AC]
  23 August 2022

Multigraded regularity of powers of two ideals on the Hirzebruch surface.

• A short resolution of the diagonal for smooth projective toric varieties of Picard rank 2
  With Michael K. Brown
  arXiv:2208.00562 [math.AG] [math.AC]
  1 August 2022

The vanishing requirements which imply a Horrocks-type splitting criterion.

• Characterizing Multigraded Regularity on Products of Projective Spaces
  With Juliette Bruce, Lauren Cranton Heller
  arXiv:2110.10705 [math.AC] [math.AG]
  20 October 2021

The twists in Beilinson’s spectral sequence corresponding to linearity and quaslinearity.

• The Virtual Resolutions Package for Macaulay2
  With Ayah Almousa, Juliette Bruce, Michael C. Loper
  Journal of Software for Algebra and Geometry, Volume 10 (2020)
  arXiv:1905.07022 [math.AG] [math.AC]
  16 May 2019

• Computations over Local Rings in Macaulay2
  arXiv:1710.09830 [math.AC]
  26 October 2017

• What is the optimal way to prepare a Bell state using measurement and feedback?
  With Leigh S. Martin, K. Birgitta Whaley
  Quantum Science and Technology, Volume 2, Number 4 (2017)
  arXiv:1704.00332 [quant-ph]
  2 April 2017

Interactions of qubits in a remote entanglement generation protocol.