Seonhee Lim

Department of Mathematical Sciences
Seoul National University

slim@snu.ac.kr

Papers   Teaching  Research

Work in progress

  1. On Subword complexity (with Donghan Kim and Olivier Carton).
  2. On Parametric geometry of numbers over global function fields (with Gukyeong Bang, Taehyeong Kim, and Frédéric Paulin).

Preprints

  1. Singular Linear Forms over Global Function Fields (with Gukyeong Bang and Taehyeong Kim), submitted. (April 2024) arXiv.
  2. Euclidean algorithms are Gaussian over imaginary quadratic fields (with Dohyeong Kim and Jungwon Lee), submitted. (Jan. 2024) arXiv.
  3. PGL2(Qp)-orbit closures on a p-adic homogeneous space of infinite volume (with Jinho Jeoung). (Nov. 2023) arXiv.
  4. Dimension estimates for badly approximable affine forms (with Taehyeong Kim and Wooyeon Kim), submitted. (Revised in Sept. 2022) arXiv. (This paper includes the content of the following preprint: arXiv.)

Accepted and published

    Recent papers

  1. Asymptotic distribution for pairs of linear and quadratic forms at integral vectors (with Jiyoung Han and Keivan Mallahi-Karai), Ergodic Theory and Dynamical Systems (published online in April 2024) online, arXiv.
  2. 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.
  3. Local limit theorem in negative curvature (with François Ledrappier), Duke Mathematical Journal (published online Jan 2021) arXiv, online. 
  4. Martin boundary of Brownian motion on Gromov hyperbolic metric graphs (with Soonki Hong), DCDS-A (published online in Jan 2021) arXiv, online.
  5. Notes on the values of volume entropy of graphs (with Wooyeon Kim), DCDS-A, Vol 40, no. 9, #2. (Sep 2020) arXiv, online. 
  6. 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. 

    7. Ergodic theory and number theory (Diophantine approximation, Oppenheim conjecture, etc.)

  7. Hausdorff dimension in inhomogeneous Diophantine approximation (with Yann Bugeaud, Dong Han Kim, and Michal Rams), IMRN (published online on 04 April 2019). arXiv online. 
  8. Dimension bound for badly approximable grids (with Nicolas de Saxce and Uri Shapira), IMRN. (published online in January 2018) arXiv, online.
  9. Equidistribution with an error rate and Diophantine approximation over function fields (with Sanghoon Kwon), Discrete and Continuous Dynamical Systems - A, 38 (published online September 2017) arXiv, online.
  10. 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 (published online October 2017) arXiv, online.
  11. 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 (December 2015), 468-506.arxiv, online
  12. Farey map, Diophantine approximation and Bruhat-Tits tree (with Dong Han Kim, Hitoshi Nakada, Rie Natsui), Finite Fields Appl. Vol. 30 (November 2014) page 14-32, arxiv, online

    13. Ergodic theory & volume entropy

  13.  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
  14.  A proof of a L1/2 ergodic theorem (joint work with F. Ledrappier), preprint. pdf (2006)
  15.  Volume entropy for hyperbolic buildings (joint work with F. Ledrappier), Journal of Modern dynamics, Volume 4, No. 1 (2010) page 139-165. arxiv, online (improved to include all regular buildings)
  16.  Minimal volume entropy for graphs, Trans. Amer. Math. Soc. 360 (2008), 5089-5100. arxiv

    17. Colorings of trees

  17. 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. 
  18. Continued fraction algorithm for Sturmian colorings of trees (with Dong Han Kim), Ergod. Th. & Dynam. Sys. (published online on 12 December 2017) arXiv,online.
  19. 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.
  20. 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.
  21. Hyperbolic tessellation and colorings of trees (with Dong Han Kim), Abstract and applied analysis, vol. 2013, ID 706496 (2013) online

    Geometric group theory

  22.  On Commensurizer Growth (joint work with Nir Avni and Eran Nevo), Israel J. Math 188. (2012) 259-279 arxiv, online
  23.  Covering theory for complexes of groups (joint work with A. Thomas), J. Pure Appl. Algebra 212 (2008) 1632-1663. arxiv
  24.  Counting overlattices for polyhedral complexes (joint work with A. Thomas), Topology Proceedings, Volume 36 (2010) page 229-247. pdf, online
  25.  Counting overlattices in automorphism groups of trees, Geom. Dedicata, Vol. 118 (2006), no. 1, pp. 1-21. arxiv

    26. Applied Mathematics

  26. 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.
  27. 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.
  28. 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).
  29. 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
  30. 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.