I am a commutative algebraist, and my research is motivated by connections with birational algebraic geometry, the theory of differential operators, classical singularity theory, and convex geometry. I am especially interested in applications of the Frobenius endomorphism and related prime characteristic methods, local cohomology, and convexity to the study of algebraic varieties.

I am an active member of Macaulay2 (M2) community. M2 is a software system devoted to supporting research in algebraic geometry and commutative algebra, and I have co-authored the following packages, which focus on explicit computation in prime characteristic, and include implementations of some of the algorithms developed in my research, but also a lot more.

• TestIdeals.m2 | M2 Documentation, GitHub
• FrobeniusThresholds.m2 | M2 Documentation, GitHub

My research is partially supported by the National Science Foundation (NSF) through the grant DMS-1902321.

• Jumping numbers of F-pure submodules
• With Alessandro De Stefani, Luis Núñez Betancourt, and Emily E. Witt.
• Submitted
• Bernstein's inequality and holonomicity for certain singular rings.
• With Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez Betancourt, Pedro Teixeira, and Emily E. Witt.
• To appear in International Mathematics Research Notices.
• https://doi.org/10.1093/imrn/rnad121
• arXiv:2103.02986
• Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands.
• With Josep Àlvarez Montaner, Jack Jeffries, Luis Núñez Betancourt, Pedro Teixeira, and Emily E. Witt.
• Commun. Contemp. Math. 24 (2022), no.10, Paper No. 2150083, 47 pp.
• arXiv:1907.10017
• The FrobeniusThresholds package for Macaulay2.
• With Karl Schwede, Pedro Teixeira, and Emily E. Witt.
• Journal of Software for Algebra and Geometry 11 (2021), no. 1, 25-39
• arXiv:1906.09491
• Frobenius powers.
• With Pedro Teixeira and Emily E. Witt.
• Math. Z. 296 (2020), no. 1-2 541-572
• arXiv:1802.02705
• The TestIdeals package for Macaulay2.
• With multiple contributors.
• J. Softw. Algebra Geom. 9-2 (2019), 89-110.
• arXiv:1810.02770
• Frobenius powers of some monomial ideals.
• With Pedro Teixeira and Emily E. Witt.
• J. Pure Appl. Algebra 224 (2020), no. 1, 66-85.
• arXiv:1808.09508
• Local Okounkov bodies and limits in prime characteristic.
• With Jack Jeffries.
• Math. Ann. 372 (2018), no. 1-2, 139-178.
• arXiv:1701.02575
• Lyubeznik numbers and injective dimension of local cohomology in mixed characteristic.
• With Luis Núñez Betancourt, Felipe Pérez, and Emily E. Witt.
• Trans. Amer. Math. Soc. 371 (2019), no. 11, 7533-7557.
• arXiv:1512.02298
• Cohomological dimension, Lyubeznik numbers, and connectedness in mixed characteristic.
• With Luis Núñez Betancourt, Felipe Pérez, and Emily E. Witt.
• J. Algebra 514 (2018), 442-467.
• arXiv:1609.05846
• On the behavior of singularities at the F-pure threshold.
• With Eric Canton, Karl Schwede, and Emily E. Witt.
• Illinois J. Math. 60 (2016), no. 3-4, 669-685.
• arXiv:1508.05427
• Local 𝔪-adic constancy of F-pure thresholds and test ideals.
• With Luis Núñez Betancourt and Emily E. Witt.
• Math. Proc. Cambridge Philos. Soc. 164 (2018), no. 2, 285-295.
• arXiv:1801.05506
• F-threshold functions: Syzygy gap fractals and the two-variable homogeneous case.
• With Pedro Teixeira.
• J. Symbolic Comput. 80 (2017), part 2, 451-483.
• arXiv:1404.5871
• F-pure thresholds of homogeneous polynomials.
• With Luis Núñez Betancourt, Emily E. Witt, and Wenliang Zhang.
• Michigan Math. J. 65 (2016), no. 1, 57-87.
• arXiv:1404.3772
• F-purity versus log canonicity for polynomials.
• Nagoya Math. J. 224 (2016), no. 1, 10-36.
• arXiv:1112.2423
• F-invariants of diagonal hypersurfaces.
• Proc. Amer. Math. Soc. 143 (2015), no. 1, 87-104.
• Journal version (updated)
• arXiv:1112.2425
• F-pure thresholds of binomial hypersurfaces.
• Proc. Amer. Math. Soc. 142 (2014), no. 7, 2227-2242.
• arXiv:1112.2427
• F-purity of hypersurfaces.
• Math. Res. Lett. 19 (2012), no. 2, 389-401.
• arXiv:1112.2424
• Log canonical thresholds, F-pure thresholds, and non-standard extensions.
• With Bhargav Bhatt, Lance Miller, and Mircea Mustaţă.
• Algebra Number Theory 6 (2012), no. 7, 1459-1482.
• arXiv:1106.0207