My main research area is knot theory and spatial graph theory. I am particularly interested in combinatorial and geometric representations of knots and links, including three-page and four-page presentations, ribbonlength, lattice embeddings, and related invariants.
A recurring theme in my work is to understand how diagrammatic and combinatorial complexity controls geometric and topological invariants.
I also work on quantum algorithms and discrete mathematical problems. My recent research includes quantum circuit design for decoding binary linear codes, quantum approaches to topological invariants, and problems in structural and spectral graph theory.
Linear upper bounds on the ribbonlength of knots and links (joint with Hyoungjun Kim and Sungjong No), Algebr. Geom. Topol. 26 (2) (2026) 553–563
New upper bounds on the ribbonlength of alternating links with bipartite dual graphs, Topology Appl. 386 (2026) 109827
Four-page index and linear upper bounds for ribbonlength, J. Knot Theory Ramifications (To appear) https://arxiv.org/abs/2602.13973
Designing quantum circuits for decoding binary linear codes (joint with Whan-Hyuk Choi and Yoonjin Lee), J. Phys. A: Math. Theor. 58(1) (2025) 015302
On the Laplacian spectrum of k-symmetric graphs (joint with Sunyo Moon), Discrete. Math. 347(1) (2024) 113681.
A diagrammatic approach to the three-page index, Osaka J. Math. (To appear) https://arxiv.org/abs/2601.12846
Fox p-Colorings as Fixed Points of Braid Representations (joint with Neungjoo Goh, Suah Jeong, Seungbin Oh), Involve (To appear) https://arxiv.org/abs/2608.29046
Four-page index and linear upper bounds for ribbonlength, J. Knot Theory Ramifications (To appear) https://arxiv.org/abs/2602.13973
New upper bounds on the ribbonlength of alternating links with bipartite dual graphs, Topology Appl. 386 (2026) 109827
Linear upper bounds on the ribbonlength of knots and links (joint with Hyoungjun Kim and Sungjong No), Algebr. Geom. Topol. 26 (2) (2026) 553–563
Three-page indices for rational links and pretzel links, J. Knot Theory Ramifications 35(1) (2026) 2550074.
Tricolorable alternating potholder diagrams, Honam Mathematical Journal 47 (2025), 530–539.
Three-page indices of torus links (joint with Useong Jang and Minseo Lee), J. Knot Theory Ramifications 34(23) (2025) 2550063.
Linking number of Montesinos links (joint with Hyoungjun Kim and Sungjong No), Topology Appl. 371(1) (2025) 109359.
Designing quantum circuits for decoding binary linear codes (joint with Whan-Hyuk Choi and Yoonjin Lee), J. Phys. A: Math. Theor. 58(1) (2025) 015302
Quantum knot mosaics and bounds of the growth constant (joint with Dooho Choi, Hyoungjun Kim and Seungsang Oh), Rev. Math. Phys. 36(10) (2024) 2450025
On the Laplacian spectrum of k-symmetric graphs (joint with Sunyo Moon), Discrete. Math. 347(1) (2024) 113681.
Topology-based optimization of handcuff graphs on 3D lattice (joint with Sungjong No and Seungsang Oh), Phys. Scr. 99(1) (2024) 015221.
Folded ribbonlength of 2-bridge knots (joint with Hyoungjun Kim and Sungjong No), J. Knot Theory Ramifications 32(04) (2023) 2350030.
Petal number of torus knots (joint with Hyoungjun Kim and Sungjong No), J. Knot Theory Ramifications 31(13) (2022) 2250096
Ribbonlength of twisted torus knots (joint with Hyoungjun Kim and Sungjong No), J. Knot Theory Ramifications 31(12) (2022) 2250092
Lattice conformation of theta-curves accompanied with Brunnian property (joint with Hyoungjun Kim, Hwa Jeong Lee, Seungsang Oh and Sungjong No), J. Phys. A: Math. Theor. 55(43) (2022) 435207
Topological aspects of theta-curves in cubic lattice (joint with Sungjong No and Seungsang Oh), J. Phys. A: Math. Theor. 54 (2021) 455204.
Lattice stick number of spatial graphs (joint with Chaeryn Lee and Seungsang Oh), J. Knot Theory Ramifications 27 (2018) 1850048.
Bisected vertex leveling of plane graphs: Braid index, arc index and delta diagrams (joint with Sungjong No and Seungsang Oh), J. Knot Theory Ramifications 27 (2018) 1850044.
Designing quantum circuits for single-deletion-correcting codes (joint with Whan-Hyuk Choi and Yoonjin Lee)
Knots and Links with Three-Page Index at Most 11 (joint with Yerin Go and Jiyu Lim)