My research is partially supported by National Science Foundation Grant DMS #1501404 / 1623035.
RESEARCH INTERESTS
Commutative algebra and its connections with algebraic geometry and representation theory.
PAPERS

Connectedness and Lyubeznik numbers

Joint with Luis NúñezBetancourt and Sandra Spiroff

Submitted for publication


Cohomological dimension, Lyubeznik numbers, and connectedness in mixed characteristic

Joint with Daniel J. Hernández, Luis NúñezBetancourt, and Felipe Pérez

Submitted for publication


Lyubeznik numbers and injective dimension in mixed characteristic

Joint with Daniel J. Hernández, Luis NúñezBetancourt, and Felipe Pérez

To appear in Transactions of the American Mathematical Society

On the behavior of singularities at the Fpure threshold

Joint with Eric Canton,
Daniel J. Hernández, and Karl Schwede

To appear in Illinois Journal of Mathematics

Local madic constancy of Fpure thresholds and test ideals

Joint with Daniel J. Hernández and Luis NúñezBetancourt

To appear in Mathematical Proceedings of the Cambridge Philosophical Society

A survey on the Lyubeznik numbers

Joint with Luis NúñezBetancourt and Wenliang Zhang

Contemporary Mathematics 657 (2016)

Fpure thresholds of homogeneous polynomials

Joint with Daniel J. Hernández, Luis NúñezBetancourt, and Wenliang Zhang

Michigan Mathematical Journal 65 (2016), 5787

Generalized Lyubeznik numbers

Joint with Luis NúñezBetancourt

Nagoya Mathematical Journal 215 (2014), 169201

Local cohomology with support in ideals of maximal minors and
submaximal Pfaffians

Joint with Claudiu Raicu and Jerzy Weyman

Advances in Mathematics 250 (2014), 596610

Lyubeznik numbers in mixed characteristic

Joint with Luis NúñezBetancourt

Mathematical Research Letters 20 (2013) no. 6, 119

Local cohomology with support in ideals of maximal minors

Advances in Mathematics 231 (2012) 19982012
SOFTWARE

TestIdeals.m2
package for positive characteristic methods in the computer algebra software Macaulay2