Research area: Commutative Algebra
My research is centered in the field of commutative algebra, with an emphasis on its connections with geometry, topology, and combinatorics. My work has a special focus on local cohomology and modules over rings of differential operators, and on understanding the positive characteristic setting. Recently I have also become interested in formal theorem provers.
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
Frobenius powers, with D. Hernández and P. Teixeira, Mathematische Zeitschrift 296 (2020), no. 1-2, 541-572
Connectedness and Lyubeznik numbers, with L. Núñez-Betancourt and S. Spiroff, International Mathematics Research Notices 2019 (2019), no. 13, 4233-4259
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.
Local cohomology with support in ideals of maximal minors, Advances in Mathematics 231 (2012) 1998-2012