My research is primarily in algebraic geometry, with interests in Brauer groups, moduli spaces and stacks, twisted sheaves, period-index problems, rationality, derived categories, and algebraic K-theory. I also work on AI-assisted mathematical research, group theory, and cryptography.
My papers and current projects are grouped below by research area.
Algebraic Geometry / Arithmetic Geometry:
Torelli theorems for moduli stacks and twisted moduli spaces of vector bundles (2026) with Soham Ghosh and Max Lieblich, preprint
Irrationality of the first stabilization of a complex smooth cubic threefold (2026) with Shitan Xu, submitted
Moduli of vector bundles on $\mu_n$-gerbes over genus 2 curves and the period-index problem (2025), submitted
Picard group action on the category of twisted sheaves (2025) with Yeqin Liu and Yu Shen, Journal of Noncommutative Geometry
Computer Science, in particular, AI applications, Machine learning, Cryptography
TwistedMerge: Certified Higher-Order Diagnostics and Abstention for Model Merging (2026), with Shitan Xu, GitHub Repo, Submitted
Albilich: Auditable Proof-State Orchestration for LLM-Based Mathematical Research (2026) with Michael Ruofan Zeng and Yong Yang, GitHub Repo, Submitted
Accelerating Finite-Field and Torus FHE via Compute-Enabled (S)RAM (2023) with Johnathan Takeshita, Dayane Reis, Michael Niemier, Sharon X. Hu, and Taeho Jung, IEEE Transaction on Computers
SLAP: Simpler, Improved Private Stream Aggregation from Ring Learning with Errors (2023) with Johnathan Takeshita, Ryan Karl, and Taeho Jung, Journal of Cryptology
Algorithmic Acceleration of B/FV like Somewhat Homomorphic Encryption for Compute-Enabled RAM (2020) with Johnathan Takeshita, Dayane Reis, Michael Niemier, Sharon X. Hu, and Taeho Jung, Selected Areas in Cryptology
Group Theory:
On intersections of system normalizers (2026) with Yuan Lu, Yong Yang and Michael Ruofan Zeng, submitted
An order automorphism of a Dlab group not induced by conjugation (2026) with Yong Yang and Michael Ruofan Zeng, currently not intended for publication.
Total 3-Closure for Projective Special Linear Groups (2026) with Yong Yang and Michael Ruofan Zeng, Preprint
Alternating Groups and Embeddings into Groups Invariably Generated by Two Prime-Order Elements (2026) with Yong Yang and Michael Ruofan Zeng, submitted
Finite Permutation Groups with Few Orbits Under the Action on the Power Set (2021) with Alex Betz, Max Chao-Haft, Thomas Michael Keller, Anthony Ter-saakov, and Yong Yang, Rocky Mountain Journal of Mathematics
On the odd order composition factors of finite linear groups (2019) with Alex Betz, Max Chao-Haft, Anthony Ter-saakov, and Yong Yang, Journal of Group Theory
I am a project leader at the UW math AI lab currently.