University of Illinois, Chicago
Office: SEO 610
Office: SEO 610
About:
I am a lecturer at the University of Illinois, Chicago. Previously, I was a Wylie Assistant Professor at the University of Utah, an NSF postdoc at UC Berkeley, and a postdoc at MSRI.
My research is in algebraic and arithmetic geometry. Among other things, I am interested in algebraic stacks, birational geometry, K3 surfaces, Brauer groups, and derived categories, particularly in mixed and positive characteristic.
Papers:
- [arXiv] Moduli of lattice-polarized K3 surfaces and boundedness of Brauer groups (with Emma Brakkee and Anthony Várilly-Alvarado). Preprint
- [arXiv] On the logarithmic Hodge-de Rham spectral sequence for curves on K3 surfaces. Preprint
- [arXiv] Ample vector bundles and moduli of tame stacks (with Martin Olsson and Rachel Webb). Preprint
- [arXiv] Murphy's Law for algebraic stacks (with Max Lieblich). Preprint
- [arXiv] Fourier-Mukai transforms commuting with Frobenius. To appear in Bulletin of the London Mathematical Society.
- [arXiv] Automorphism groups of curves over arbitrary fields. Preprint
- [arXiv] Projectivity of the moduli space of vector bundles on a curve (with Jarod Alper, Pieter Belmans, Jason Liang, and Tuomas Tajakka). In Stacks Project Expository Collection, Eds. Belmans, P., Ho, W., & De Jong, A., London Mathematical Society Lecture Note Series (2022), Cambridge University Press.
- [arXiv] Unipotent morphisms (with Jack Hall and Siddharth Mathur). To appear in Geometry & Topology.
- [arXiv] Representability of cohomology of finite flat abelian group schemes (with Martin Olsson). Preprint
- [arXiv] Hodge numbers are not derived invariants in positive characteristic (with Nicolas Addington). Mathematische Annalen, Vol. 387 (2023); pgs 847-878.
- [arXiv] Twisted derived equivalences and isogenies between K3 surfaces in positive characteristic (with Ziquan Yang). Algebra and Number Theory, Vol. 17 no. 5 (2023); pgs 1069–1126.
- [arXiv] Lifts of twisted K3 surfaces to characteristic 0. International Mathematical Research Notices, Vol. 5 (2023); pgs 4337–4407.
- [arXiv] Derived invariants from topological Hochschild homology (with Benjamin Antieau). Algebraic Geometry, Vol. 9 no. 3 (2022); pgs 364-399.
- [arXiv] Perfect points on genus one curves and consequences for supersingular K3 surfaces (with Max Lieblich). Compositio Mathematica, Vol. 158 no. 5 (2022); pgs 1052-1083.
- [arXiv] Derived equivalences of twisted supersingular K3 surfaces. Advances in Mathematics, Vol. 378 (2021); 107498.
- [arXiv] Twistor spaces for supersingular K3 surfaces (with Max Lieblich). Preprint
- [arXiv] Restrictions of rainbow supercharacters (with Nathaniel Thiem). Journal of Algebra, Vol. 451 (2016); pgs 357-400.