Research
My primary research interest lies in algebraic number theory and arithmetic statistics.
Some of the projects I was involved in during my military service span a number of topics in graph neural networks and industrial mathematics.
Any comments are welcome!
Number theory / Arithmetic Statistics
A geometric approach to prime Selmer groups of cyclic prime twist families of elliptic curves (2024, In preparation)
Counting poins on x^2 + y^2 = z^4 and 5-isogenies of elliptic curves over Q, coauthored with Santiago Arango-Piñeros, Changho Han, and Oana Padurariu (2024, In preparation)
On the prime Selmer groups of cyclic prime twist families of elliptic curves over global function fields (2022, Submitted). (Slides) (Caricature)
A1-homotopy degree of covering maps of modular curves, coauthored with Hyun Jong Kim. (2021, Submitted)
On the average p-Selmer rank in quadratic twist families of elliptic curves over global function fields, coauthored with Niudun Wang. (2023, International Mathematics Research Notices) (Slides)
Polynomial relations between operators on chains of representation rings, coauthored with Maithreya Sitaraman. (2022, Communications in Algebra)
Minimum degrees of algebraic numbers with respect to primitive elements, coauthored with Cheol-Min Park. (2021, International Journal of Number Theory)
Graph Neural Networks
Topology-informed graph transformer, coauthored with Yun Young Choi, Minho Lee, and Youngho Woo (2024, Submitted)
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, Submitted)
A functorial formulation of neighborhood aggregating deep learning, coauthored with Yun Young Choi, U Jin Choi, and Youngho Woo (2023, In preparation)
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, Accepted to ICLR 2023) (Video Recording)
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)
Industrial Mathematics
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)
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)
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)