Research Questions, Et Cetera
My current projects all involve commutative algebra over Cox rings of projective varieties.
See my oral exam presentation for some topics and questions that lead me to this point.
Publications and preprints
 Bounds on Multigraded Regularity
With Juliette Bruce, Lauren Cranton Heller.
Submitted. 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 proj. toric varieties of Picard rank 2
With Michael K. Brown.
To appear in Algebra & Number Theory.
arXiv:2208.00562 [math.AG] [math.AC]
1 August 2022
The vanishing requirements which imply a Horrockstype splitting criterion.
 Characterizing Multigraded Regularity on Products of Projective Spaces
With Juliette Bruce, Lauren Cranton Heller.
Submitted. arXiv:2110.10705 [math.AC] [math.AG]
20 October 2021
The terms in Beilinsonâ€™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
A virtual resolution for 3 points in $\PP^1\times\PP^1$ as a subcomplex of the minimal free resolution.

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 [quantph]
2 April 2017
Interactions of qubits in a remote entanglement generation protocol.