Research

My field of study is algebraic geometry and commutative algebra in positive characteristic, with a focus on F-singularity theory and F-invariants such as test ideals and F-signature. Generally speaking, I'm interested in any algebraic geometry that has to do with the Frobenius morphism. I'm also interested in their interaction with characteristic zero algebraic geometry, e.g. singularities in the MMP and multiplier ideals. My research preprints.

List of publications

Preprints and submitted papers:

  • On the behavior of stringy motives under Galois quasi-étale covers, w/ T. Yasuda. arXiv:2105.05214.

  • On the local étale fundamental group of KLT threefold singularities, w/ A. Stäbler and w/ an appendix by J. Kollár . arXiv:2004.07628.

  • Tame fundamental groups of pure pairs and Abhyankar's lemma, w/ A. Stäbler. arXiv:1910.02111.

  • On the behavior of F-signatures, splitting primes, and test modules under finite covers, w/ A. Stäbler. arXiv:1904.10382.

  • Finite torsors over strongly F-regular singularities. arXiv:1710.06887.

You can find a copy of Ph.D. Thesis here. It is the version with working links and hyperref (I couldn't include these features in the offical version due to UUtah's particular editorial rules). The official, ProQuest's version can (possibly) be found here.

Conference Posters:

  • Fundamental groups of F-regular singularities via F-signature. (PDF)

  • Finite torsors over strongly F-regular singularities. (PDF)