Group actions on homogeneous spaces and applications to number theory
Lattices of Lie groups and automorphism groups of trees and polyhedral complexes
Dynamics of group actions on trees and buildings, more generally, metric spaces of non-positive curvature
Entropy rigidity, thermodynamics formalism
Singular Linear Forms over Global Function Fields (with Gukyeong Bang and Taehyeong Kim), to appear in Journal of Number Theory. (Nov 2025+) arXiv.
Euclidean algorithms are Gaussian over imaginary quadratic fields (with Dohyeong Kim and Jungwon Lee), Journal of LMS. (Dec. 20, 2025) online, arXiv.
Dimension estimates for badly approximable affine forms (with Taehyeong Kim and Wooyeon Kim), Ergodic Theory and Dynamical Systems. (Nov. 06, 2024) published online, arXiv. (This paper includes the content of the following preprint: arXiv.)
Asymptotic distribution for pairs of linear and quadratic forms at integral vectors (with Jiyoung Han and Keivan Mallahi-Karai), Ergodic Theory and Dynamical Systems ( April 17, 2024) online, arXiv.
PGL2(Qp)-orbit closures on a p-adic homogeneous space of infinite volume (with Jinho Jeoung). (preprint Nov. 2023) arXiv.
Homogeneous dynamics and number theory (Diophantine approximation, Oppenheim conjecture, etc.)
On Hausdorff dimension in inhomogeneous Diophantine approximation over global function fields (with Taehyeong Kim and Frédéric Paulin), J. Number Theory. Vol 251, pp. 102-146 (October 2023) arXiv.
Limiting distribution of geodesics in a geometrically finite quotients of regular trees (with Sanghoon Kwon), Groups Geom. Dyn. 15 (2021), no. 1, pp. 35–55 (Dec. 2020) online. arXiv.
Hausdorff dimension in inhomogeneous Diophantine approximation (with Yann Bugeaud, Dong Han Kim, and Michal Rams), IMRN (04 April 2019). online, arXiv .
Dimension bound for badly approximable grids (with Nicolas de Saxce and Uri Shapira), IMRN. (January 2018) arXiv, online.
Equidistribution with an error rate and Diophantine approximation over function fields (with Sanghoon Kwon), Discrete and Continuous Dynamical Systems - A, 38 (September 2017), online, arXiv.
Asymptotic distribution of values of isotropic quadratic forms at S-integral points (with Keivan Mallahi-Karai and Jiyoung Han), Journal of Modern Dynamics. vol. 11, 501-550 (October 2017), online, arXiv.
Distribution of integral lattice points in an ellipsoid with a diophantine center (with Jiyoung Han, Hyunsuk Kang, Yong-Cheol Kim) J. Number theory vol. 157 , 468-506 (December 2015). online, arxiv.
Farey map, Diophantine approximation and Bruhat-Tits tree (with Dong Han Kim, Hitoshi Nakada, Rie Natsui), Finite Fields Appl. Vol. 30, page 14-32 (November 2014), online, arxiv.
Local limit theorem in negative curvature (with François Ledrappier), Duke Mathematical Journal (Jan 2021), online, arXiv.
Martin boundary of Brownian motion on Gromov hyperbolic metric graphs (with Soonki Hong), DCDS-A (Jan 2021), online, arXiv.
Notes on the values of volume entropy of graphs (with Wooyeon Kim), DCDS-A, Vol 40, no. 9, #2. (Sep 2020) online, arXiv.
On the distribution of orbits of geometrically finite hyperbolic groups on the boundary (with Hee Oh), Ergod. Th. & Dynam. Sys., Vol 32 (2011), 173-189. online, arxiv
A proof of a L1/2 ergodic theorem (joint work with F. Ledrappier), preprint. pdf (2006)
Volume entropy for hyperbolic buildings (joint work with F. Ledrappier), Journal of Modern Dynamics, Volume 4, No. 1 (2010), pages 139-165. online, arxiv (improved to include all regular buildings)
Minimal volume entropy for graphs, Trans. Amer. Math. Soc. 360 (2008), 5089-5100. arxiv
Quasi-Sturmian colorings on trees (with Dong Han Kim, Seulbee Lee, Deokwon Shim), Ergod. Th. & Dynam. Sys. (published online on 09 Aug 2019). arXiv online.
Continued fraction algorithm for Sturmian colorings of trees (with Dong Han Kim), Ergod. Th. & Dynam. Sys. (published online on 12 December 2017) arXiv, online.
Colorings of trees with linear, intermediate and exponential subword complexity (with Seulbee Lee), J. Korean Math. Soc. Vol. 52, No. 6, 1123-1137 (November 2015) online.
Subword complexity and Sturmian colorings of trees (with Dong Han Kim), Ergod. Th. & Dynam. Sys. Vol 35, no. 2 (April 2015) 461-481. arxiv, online.
Hyperbolic tessellation and colorings of trees (with Dong Han Kim), Abstract and applied analysis, vol. 2013, ID 706496 (2013) online
On Commensurizer Growth (joint work with Nir Avni and Eran Nevo), Israel J. Math 188. (2012) 259-279 arxiv, online
Covering theory for complexes of groups (joint work with A. Thomas), J. Pure Appl. Algebra 212 (2008) 1632-1663. arxiv
Counting overlattices for polyhedral complexes (joint work with A. Thomas), Topology Proceedings, Volume 36 (2010) page 229-247. pdf, online
Counting overlattices in automorphism groups of trees, Geom. Dedicata, Vol. 118 (2006), no. 1, pp. 1-21. arxiv
Triple network activation causes tinnitus in patients with sudden sensorineural hearing loss: A model-based volume-entropy analysis (with Seung Jae Lee, Jaemin Park, Sang-Yeon Lee, Ja-Won Koo, Sven Vanneste, Dirk De Ridder, Jae-Jin Song), Frontiers in Neuroscience (published Nov. 2022) online.
Topological Data Analysis of Coronary Plaques Demonstrates the Natural History of Coronary Atherosclerosis (with Doyeon Hwang, Haneol Kim, Seung-Pyo Lee, et al.) JACC Cardiovasc Imaging (accepted Jan 2021) online.
Maturational delay and asymmetric information flow of brain connectivity in SHR model of ADHD revealed by topological analysis of metabolic networks (by Seunggyun Ha, Hyekyoung Lee, Yoori Choi, Hyejin Kang, Se Jin Jeon, Jong Hoon Ryu, Hee Jin Kim, Jae Hoon Cheong, Seonhee Lim, Bungnyun Kim, and Dong Soo Lee), accepted to Scientific Reports (Jan 2020).
Volume entropy for modeling information flow in a brain graph (with Heykyoung Lee, Eunkyung Kim, Youngmin Huh, Youngjo Lee, and Dong Soo Lee), Scientific Reports. (published online on 22 Jan 2019) arXiv. online
Integrated multimodal network approach to PET and MRI based on multidimensional persistent homology (with Hyekyong Lee, Dong Soo Lee et al.), Human Brain Mapping (November 2016) arxiv, online.