RESEARCH INTERESTS

• Commutative algebra and its interactions with algebraic geometry, representation theory, and singularity theory

SOFTWARE

• FrobeniusThresholds  |  Current version:   2.0  |  Certified in 2020  |  Github
• TestIdeals  |  Current version:   1.01  |  Certified in 2019  |  Github

PAPERS

My research is partially supported by NSF CAREER Award DMS-1945611

• Local cohomology of subspace arrangements and simplicial homology, with A. Pascoe, submitted (32 pages)
• Jumping numbers of F-pure submodules, with A. De Stefani, D. J. Hernández, and L. Núñez-Betancourt, submitted (26 pages)
• Formalizing Commutative Algebra in Coq:   Nakayama's Lemma, with D. Cousino and P. Alexander submitted (12 pages)
• Bernstein's inequality and holonomicity for certain singular rings, with J. Àlvarez Montaner, J. Jeffries, D. J. Hernández, L. Núñez-Betancourt, and P. Teixeira, to appear in International Mathematics Research Notices
• Lower bounds on the F-pure threshold and extremal singularities, with Z. Kadyrsizova, J. Kenkel, J. Page, J. Singh, K. E. Smith, and A. Vraciu, to appear in Transactions of the American Mathematical Society, 9 (2022), 977-1005
• Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands, with J. Àlvarez Montaner, J. Jeffries, D. J. Hernández, L. Núñez-Betancourt, and P. Teixeira, Communications in Contemporary Mathematics 24 (2022), no. 10, Paper No. 2150083, 47 pp.
• Classifications of Frobenius forms in five variables, with Z. Kadyrsizova, J. Kenkel, J. Page, J. Singh, K. E. Smith, and A. Vraciu, Women in Commutative Algebra , Springer, AWM Series 29 (2021), 353-367
• Cubic surfaces of characteristic two, with Z. Kadyrsizova, J. Kenkel, J. Page, J. Singh, K. E. Smith, and A. Vraciu, Transactions of the American Mathematical Society 374 (2021), 6251-6267
• The FrobeniusThresholds package for Macaulay2, with D. Hernández, K. Schwede, and P. Teixeira, Journal of Software for Algebra and Geometry 11 (2021), no. 1, 25-39
• Frobenius powers, with D. Hernández and P. Teixeira, Mathematische Zeitschrift 296 (2020), no. 1-2, 541-572
• Frobenius powers of some monomial ideals, with D. Hernández and P. Teixeira, Journal of Pure and Applied Algebra 224 (2020) no. 1, 66-85
• Connectedness and Lyubeznik numbers, with L. Núñez-Betancourt and S. Spiroff, International Mathematics Research Notices 2019 (2019), no. 13, 4233-4259
• Lyubeznik numbers and injective dimension in mixed characteristic, with D. J. Hernández, L. Núñez-Betancourt, and F. Pérez, Transactions of the American Mathematical Society 371 (2019) no. 11, 7533-7557
• The TestIdeals package for Macaulay2, with A. Boix, D. Hernández, Z. Kadyrizova, M. Katzman, S. Malec, M. Robinson, K. Schwede, D. Smolkin, and P. Teixeira, Journal of Software for Algebra and Geometry 9 (2019), no. 2, 89-110
• Cohomological dimension, Lyubeznik numbers, and connectedness in mixed characteristic, with D. J. Hernández, L. Núñez-Betancourt, and F. Pérez, Journal of Algebra 514 (2018), 442-467
• Local m-adic constancy of F-pure thresholds and test ideals, with D. J. Hernández and L. Núñez-Betancourt, Mathematical Proceedings of the Cambridge Philosophical Society 164 (2018) no. 2, 285-295
• On the behavior of singularities at the F-pure threshold, with E. Canton, D. J. Hernández, and K. Schwede, Illinois Journal of Mathematics 60 (2016), no. 3-4, 669-685
• A survey on the Lyubeznik numbers, with L. Núñez-Betancourt and W. Zhang, Contemporary Mathematics (AMS) 657 (2016), 137-163
• F-pure thresholds of homogeneous polynomials, with D. J. Hernández, L. Núñez-Betancourt, and W. Zhang, Michigan Mathematical Journal 65 (2016), 57-87
• Generalized Lyubeznik numbers, with L. Núñez-Betancourt, Nagoya Mathematical Journal 215 (2014), 169-201
• Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians, with C. Raicu and J. Weyman, Advances in Mathematics 250 (2014), 596-610.
• Lyubeznik numbers in mixed characteristic, with L. Núñez-Betancourt, Mathematical Research Letters 20 (2013) no. 6, 1-19.
• Local cohomology with support in ideals of maximal minors, Advances in Mathematics 231 (2012) 1998-2012