Research

I'm currently interested in positive characteristic algebraic geometry and commutative algebra, with a focus on Fano geometry and the geometry of Frobenius endomorphisms. That is, I'm interested in Frobenius actions on Fano-type varieties and their singularities as well as objects and concepts defined via Frobenius actions, e.g. F-singularity theory, ordinarity, etc. My research concentrates on the study of Fano varieties and KLT singularities via globally F-regular varieties, strongly F-regular singularities, test and multiplier ideals, stringy motives, Kollár components, and étale fundamental groups. My research preprints.

List of publications

• On the local étale fundamental group of KLT threefold singularities, w/ A. Stäbler and w/ an appendix by J. Kollár . Algebraic Geometry 10 (6) (2023) 694–728. DOI: 10.14231/AG-2023-025

• Singularities of determinantal pure pairs, w/ A. Vilpert. Boll Unione Mat Ital (2023) DOI: 10.1007/s40574-023-00361-z

• Tame fundamental groups of pure pairs and Abhyankar's lemma, w/ A. Stäbler. Algebra & Number Theory, Vol. 17 (2023), No. 2, 309–358. DOI: 10.2140/ant.2023.17.309

• On the behavior of F-signatures, splitting primes, and test modules under finite covers, w/ A. Stäbler. Journal of Pure and Applied Algebra, Volume 227, Issue 1, January 2023, 107165. DOI: 10.1016/j.jpaa.2022.107165

• Finite torsors over strongly F-regular singularities. Épijournal de Géométrie Algébrique, March 1, 2022, Volume 6. DOI: 10.46298/epiga.2022.7532

• Covers of rational double points in mixed characteristic, w/ L. Ma, T. Polstra, K. Schwede, and K. Tucker. Journal of Singularities, volume 23 (2021), 127-150. DOI: 10.5427/jsing.2021.23h

• Bertini Theorems for F-signature and Hilbert–Kunz multiplicity, w/ K. Schwede and K. Tucker. Math. Z. (2021). DOI: 10.1007/s00209-021-02712-y

• The uniform symbolic topology property for diagonally F-regular algebras, w/ D. Smolkin. Journal of Algebra 548 (2020) 25–52. DOI: 10.1016/j.jalgebra.2019.11.017

• Étale fundamental groups of strongly F-regular schemes, w/ B. Bhatt, P. Graf, K. Schwede and K. Tucker. IMRN, Volume 2019, Issue 14, July 2019, Pages 4325–4339. DOI: 10.1093/imrn/rnx253

• Fundamental groups of F-regular singularities via F-signature, w/ K. Schwede and K. Tucker. Ann. Sci. Éc. Norm. Supér. (4) 51 (2018), no. 4, 993–1016. DOI: 10.24033/asens.2370

• On the monotonicity of the correction term in Ramanujan's factorial approximation, w/ M. B. Villarino and D. Campos Salas. The Mathematical Gazette; July 2013, Vol. 97 Issue 539, p. 274. DOI: 10.1017/S002555720000591X

Preprints and submitted papers:

• On tame ramification and centers of F-purity, w/ A. Fayolle. arXiv:2308.02660. Anne made this nice POSTER about it.

• Varieties with ample Frobenius-trace kernel, w/ Zs. Patakfalvi. arXiv:2110.15035. You can watch a talk I gave about this paper at Princeton here.

• On the behavior of stringy motives under Galois quasi-étale covers, w/ T. Yasuda. arXiv:2105.05214. You can watch Takehiko's talk at ZAGS on this paper here!

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)