RESEARCH INTERESTS

Commutative algebra and its interactions with algebraic geometry,
representation theory, and singularity theory
SOFTWARE
Coauthor of the following packages for the opensource software system
Macaulay2 devoted to supporting research
in algebra and algebraic geometry:
PAPERS
My research is partially supported by NSF CAREER Award DMS1945611
Bernstein's
inequality and holonomicity for certain singular rings, with J. Àlvarez Montaner, J.
Jeffries, D. J. Hernández, L.
NúñezBetancourt, and P. Teixeira, submitted (2021)
Lower bounds on the Fpure 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
BernsteinSato functional equations,
Vfiltrations, and multiplier ideals of direct summands,
with J. Àlvarez Montaner, J. Jeffries, D.
J. Hernández, L. NúñezBetancourt, and P.
Teixeira,
to appear in Communications in Contemporary Mathematics
Classifications of Frobenius forms in five
variables, with Z. Kadyrsizova, J. Kenkel, J. Page, J. Singh,
K. E. Smith, and A. Vraciu,
to appear in Springer AWM Series
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), 62516267
The
FrobeniusThresholds package for Macaulay2,
with D. Hernández, K. Schwede, and P. Teixeira,
Journal of Software for Algebra and Geometry 11 (2021), no. 1, 2539
Frobenius powers,
with D. Hernández and
P. Teixeira, Mathematische Zeitschrift 296 (2020), no. 12, 541572
Frobenius
powers of some monomial ideals,
with D. Hernández and P. Teixeira,
Journal of Pure
and Applied Algebra 224 (2020) no. 1, 6685
Connectedness and Lyubeznik numbers,
with L. NúñezBetancourt and S. Spiroff,
International Mathematics Research Notices 2019 (2019),
no. 13, 42334259
Lyubeznik
numbers and injective dimension in mixed characteristic, with D. J. Hernández, L. NúñezBetancourt,
and F. Pérez,
Transactions of the American Mathematical Society 371
(2019) no. 11, 75337557
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, 89110
Cohomological dimension, Lyubeznik numbers, and
connectedness in mixed characteristic,
with D. J. Hernández, L. NúñezBetancourt,
and F. Pérez,
Journal of Algebra 514 (2018), 442467
Local
madic constancy of Fpure thresholds and test
ideals,
with D. J. Hernández and L.
NúñezBetancourt,
Mathematical Proceedings of the
Cambridge Philosophical Society 164 (2018) no. 2, 285295
On the
behavior of singularities at the Fpure threshold,
with E. Canton, D. J. Hernández, and K. Schwede,
Illinois Journal of Mathematics 60 (2016), no. 34, 669685
A survey on
the Lyubeznik numbers,
with L. NúñezBetancourt and W. Zhang,
Contemporary Mathematics (AMS) 657 (2016), 137163
Fpure
thresholds of homogeneous polynomials,
with D. J. Hernández, L. NúñezBetancourt,
and W. Zhang,
Michigan Mathematical Journal 65 (2016), 5787
Generalized
Lyubeznik numbers,
with L. NúñezBetancourt,
Nagoya Mathematical Journal 215 (2014), 169201
Local
cohomology with support in ideals of maximal minors and submaximal
Pfaffians,
with C. Raicu and J. Weyman,
Advances in Mathematics 250 (2014), 596610.
Lyubeznik
numbers in mixed characteristic,
with L. NúñezBetancourt,
Mathematical Research
Letters 20 (2013) no. 6, 119.
Local
cohomology with support in ideals of maximal minors,
Advances in Mathematics 231 (2012) 19982012