Research interests
I am interested in singularities in algebraic geometry, Hodge theory and algebraic K-theory. In particular, I am trying to understand the higher rational and higher Du Bois singularities that were introduced recently as a refinement of rational and Du Bois singularities. I'm also interested in applications of Hodge theory to the algebraic K-theory of singular varieties.
Papers and preprints
- (with Matthew Satriano) K-regularity for finite quotient singularities, preprint.
- (with Andrew Burke and Mihnea Popa) Negative K-theory and Hodge theory, submitted.
- (with M. Batavia, C. Chen, A. Chlopecki, T. Duff, W. Huang, A. Li and I. Nometa) A Macaulay2 package on Elimination Templates, submitted.
- On higher Du Bois singularities and K-regularity, to appear in Compositio Mathematica.
- (with Mihnea Popa and Anh Duc Vo) Injectivity and vanishing for the Du Bois complexes of isolated singularities, Algebra and Number Theory, 2026.
- (with Mihnea Popa) Du Bois complexes of cones over singular varieties, local cohomological dimension, and K-groups, Rev. Roumaine Math. Pures Appl., L. Badescu memorial volume, 2025.
- (with Sridhar Venkatesh and Anh Duc Vo) On k-Du Bois and k-rational singularities, to appear in Ann. Inst. Fourier.
- (with Sridhar Venkatesh and Anh Duc Vo) Local vanishing for toric varieties, Manuscripta Mathematica, 2024.
- (with Kathryn Hare and Kevin Hare) The Lq-spectrum for a class of self-similar measures with overlap, Asian Journal of Mathematics, 2021.
- (with Jenna Rajchgot and Matthew Satriano) Some combinatorial cases of the three matrix analog of Gerstenhaber’s theorem, Proceedings of the 2019 AWM.
- (with Kathryn Hare, Kevin Hare and Brian Morris) The entropy of Cantor-like measures, Acta Mathematica Hungarica, 2019.