My primary research interest lies in number theory and arithmetic statistics.
Some of the projects I was involved in since my military service span a number of topics in graph neural networks and industrial mathematics.
Any comments are welcome!
Publications and preprints in number theory & arithmetic statistics
[16] Rank growth of elliptic curves over cyclic extensions of function fields, coauthored with Wanlin Li (2026, In Progress. Draft available upon request).
[15] Unexpected primes of good reduction in quotients of modular and Shimura curves, coauthored with Oana Padurariu and John Voight (2026, Preprint).(Github)
[14] Distribution of Selmer ranks in prime cyclic extensions, coauthored with Daniel Keliher (2026, Preprint). (Oberwolfach Report) (Lecture notes at CRM)
[13] Secondary terms for first moments of prime Selmer groups of twists of elliptic curves over global function fields (2026, Submitted).
[12] Orbit Decomposition statistics for discrete dynamical systems: the Cesàro mean and a large deviation principle, coauthored with Gunther Cornelissen (2026, Submitted).
[11] On the application of large deviation estimates to local solubility in families of varieties, coauthored with Efthymios Sofos (2025, Submitted).
[10] Large deviation principles for abelian monoids, coauthored with Daniel Keliher (2026, Electronic Communications in Probability).
[9] Infinitely many genus two and three curves of small fixed positive rank, coauthored with Stevan Gajovic (2025, Submitted).
[8] Mordell-Lang and disparate Selmer ranks of odd twists of some superelliptic curves over global function fields (2025, Submitted).
[7] Counting 5-isogenies of elliptic curves over Q, coauthored with Santiago Arango-Piñeros, Changho Han, and Oana Padurariu (2026, Journal of the London Mathematical Society).
[6] Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents, coauthored with Daniel Keliher (2025, Submitted).
[5] On the prime Selmer groups of cyclic prime twist families of elliptic curves over global function fields (2025, Compositio Mathematica). (Slides) (Caricature)
[4] A1-homotopy degree of covering maps of modular curves, coauthored with Hyun Jong Kim. (2021, Submitted)
[3] On the average p-Selmer rank in quadratic twist families of elliptic curves over global function fields, coauthored with Niudun Wang. (2024, International Mathematics Research Notices) (Slides)
[2] Polynomial relations between operators on chains of representation rings, coauthored with Maithreya Sitaraman. (2022, Communications in Algebra)
[1] Minimum degrees of algebraic numbers with respect to primitive elements, coauthored with Cheol-Min Park. (2021, International Journal of Number Theory)
PhD Thesis
Arithmetic statistics of Selmer groups of twist families of elliptic curves over global fields (2024).
Chapter 2: Subsumed to "On the prime Selmer groups of cyclic prime twist families of elliptic curves over global function fields''.
Chapter 3: Corrigendum. Subsumed to ``Secondary terms for first moments of prime Selmer groups of cyclic prime twist families of elliptic curves over global function fields'', and other ongoing works in progress.
Chapter 4: Subsumed to ``Rank growth of elliptic curves over S3 extensions with fixed quadratic resolvents'' in joint work with Daniel Keliher, and other ongoing works in progress.
Publications and preprints in artificial intelligence
[AI5] A functorial formulation of neighborhood aggregating deep learning, coauthored with Yun Young Choi, U Jin Choi, and Youngho Woo (2026, Submitted)
[AI4] Topology-informed graph transformer, coauthored with Yun Young Choi, Minho Lee, and Youngho Woo (2024, ICML 2024 GRaM Workshop)
[AI3] A Gated MLP architecture for learning Topological dependencies in spatio-temporal graphs, coauthored with Yun Young Choi, Minho Lee, Seunghwan Lee, and Joohwan Ko (2024, LOG2024)
[AI2] Cycle to Clique (Cy2C) Graph Neural Network: A Sight to See beyond Neighborhood Aggregation, coauthored with Yunyoung Choi, U Jin Choi, and Youngho Woo (2023, ICLR 2023) (Video Recording)
[AI1] The PWLR graph representation: A persistent Weisfeiler-Lehman scheme with random walks for graph classification, coauthored with Yunyoung Choi, Dosang Joe, U Jin Choi, and Youngho Woo (2022, Conference Proceeding: PMLR Volume 196: Topological, Algebraic, and Geometric Learning Workshops) (Poster)
Publications in industrial mathematics
[IM3] A novel ageing parameter for online estimation of Lithium-ion battery states of charge and health, coauthored with Hyunju Lee and Yongsul Won (2022, Journal of Energy Storage)
[IM2] On the application of matrix congruence to QUBO formulations for systems of linear equations, coauthored with Hyunju Lee, Byung Chun Kim, Youngho Woo, and Kyungtaek Jun. (2021, Conference Proceeding: The 12th International Conference on Information and Communication Technology Convergence)
[IM1] Circuit depth reduction algorithm for QUBO and Ising models in gate-model quantum computers, coauthored with Hyunju Lee, Byung Chun Kim, Youngho Woo, and Kyungtaek Jun. (2021, Conference Proceeding: The 12th International Conference on Information and Communication Technology Convergence)