Hyungryul Harry BaikDepartment of Mathematical Sciences · KAIST
HYUNGRYUL HARRY BAIK / PUBLICATIONS

Publications

See all my preprints on arXiv here.  Here is my Google Scholar page. 

Published/Accepted Papers 

3(or higher)-Manifolds (flows, laminations, foliations, geometry and topology of mapping tori) 

  1. Characterization of Fuchsian Groups as Laminar Groups & the Structure Theorem of Hyperbolic 2-Orbifolds (with K. Kim), to appear in Glasnik Matematicki. arXiv:2110.06481. [Samsung]

  2. Groups acting on veering pairs and Kleinian groups (with H. Jung, K. Kim), J. Lond. Math. Soc. 111(1), e70052 (2025), DOI 10.1112/jlms.70052 . [ arXiv ], [ Journal Link ] . [Samsung] [DOI]

  3. On the asymptotic translation lengths on the sphere complexes and the generalized fibered cone (with D.M. Kim, C. Wu), Trans. Amer. Math. Soc., Volume 378, Number 7, 2025, Pages 4739–4764. [ arXiv ], [Journal Link ] . [NRF20] [DOI]

  4. Asymptotic translation lengths and normal generation for pseudo-Anosov monodromies of fibered 3-manifolds (with E. Kin, H. Shin, C. Wu), Algebr. Geom. Topol. 23-3 (2023), 1363--1398 [ arXiv ], [ Journal Link ] . [Samsung] [DOI]

  5. Foliations from left orders (with S. Hensel, C. Wu), J. Korean Math. Soc. 2022; 59(4): 699-715 [ arXiv ], [ Journal Link ]. [Samsung]

  6. An upper bound on the asymptotic translation lengths on the curve graph and fibered faces (with H. Shin, C. Wu), Indiana Univ. Math. J. (2021), 70 No. 4, pp. 1625–1637. [ arXiv ] , [ Journal Link ]. [Samsung] [DOI]

  7. Laminar groups and 3-manifolds (with K. Kim), Ohshika, Ken’ichi, and Athanase Papadopoulos, eds. In the Tradition of Thurston: Geometry and Topology. Springer Nature, 2020, pp. 365–421. [ arXiv ], [ Book Link] [Samsung] [DOI]

  8. The smallest positive eigenvalue of fibered hyperbolic 3-manifolds (with I. Gekhtman, U. Hamenstädt), Proc. Lond. Math. Soc. (2020), Volume 120, Issue 5, pp. 704-741. [ arXiv ], [ Journal Link ]. [DOI]

  9. Exponential torsion growth for random 3-manifolds (With D. Bauer, I. Gekhtman, U. Hamenstädt, S. Hensel, T. Kastenholz, B. Petri, D. Valenzuela), Int. Math. Res. Not. IMRN. Volume 2018, Issue 21, pp. 6497–6534. [ arXiv ] [ Journal Link ] [DOI]


Surfaces, Mapping Class Groups, and Teichmüller Theory/Dynamics

  1. Normal generators for mapping class groups (with D. M. Kim), forthcoming chapter in In the Tradition of Thurston: Geometry and Topology, Vol. 4 (edited by A. Papadopoulos and K. Ohshika). arXiv:2504.14759 . [NRF25]

  2. Simple length spectra as moduli for hyperbolic surfaces and rigidity of length identities (with I. Choi, D. M. Kim), to appear in Ann. Inst. Fourier. [ arXiv ] . [Samsung], [NRF25]

  3. Minimal asymptotic translation lengths on curve complexes and homology of mapping tori (with D. M. Kim, C. Wu), Michigan Math. J. 75(5): 927-942 (2025) [ arXiv ], [ Journal Link ]. [NRF20] [DOI]

  4. Reducible normal generators for mapping class groups are abundant (with D.M. Kim, C. Wu), J. Topol. Anal. Vol. 17, No. 05, pp. 1313-1323 (2025) [ arXiv ], [ Journal Link ]. [NRF20] [DOI]

  5. On Translation Lengths of Pseudo-Anosov Maps on the Curve Graph (with C. Kim), Bull. Korean Math. Soc. 61 (2024), No. 3, pp. 585–595 [ arXiv ], [ Journal Link ] . [NRF20]

  6. Topological and dynamical properties of Torelli groups of partitioned surfaces (with H. Shin, P. Tranchida), Geom. Dedicata. 218, 38 (2024) [ arXiv ], [ Journal Link ]. [NRF20] [DOI]

  7. Random walks on mapping class groups (with I. Choi), EMS Surv. Math. Sci. 9 (2022), no. 2, pp. 279–320 [ arXiv ], [ Journal Link ]. [NRF20] [DOI]

  8. On the surjectivity of the symplectic representation of the mapping class group (with I. Choi, D. M. Kim), Topol. Appl. 322 (2022): 108334 [ arXiv ] , [Journal Link ]. [Samsung] [DOI]

  9. Topological entropy of pseudo-Anosov maps from a typical Thurston’s construction (with I. Choi, D. M. Kim), Int. Math. Res. Not. IMRN (2022), no.24, 19862–19904 [ arXiv ], [ Journal Link ]. [Samsung]

  10. Topological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori (with J. Baik, C. Kim, P. Tranchida), Glasnik Matematicki (2022), Vol. 57(77), 291-312 [ arXiv ], [ Journal Link ]. [Samsung] [DOI]

  11. On translation lengths of Anosov maps on the curve graph of the torus (with C. Kim, S. Kwak, H. Shin), Geom. Dedicata (2021), 214, pp. 399–426. [ arXiv ], [ Journal Link ]. [Samsung] [DOI]

  12. Minimal asymptotic translation lengths of Torelli groups and pure braid groups on the curve graph (with H. Shin), Int. Math. Res. Not. IMRN (2020), Volume 2020, Issue 24, pp. 9974–9987. [ arXiv ], [ Journal Link ]. [Samsung]

  13. Is a typical bi-Perron algebraic unit a pseudo-Anosov dilatation? (with A. Rafiqi, C. Wu), Ergod. Theory Dyn. Syst. (2019), Volume 39, Issue 7, pp. 1745-1750. [ arXiv ], [ Journal Link ]. [ERC] [DOI]

  14. Constructing pseudo-Anosov maps with given dilatations (with A. Rafiqi and C. Wu), Geom. Dedicata (2016), Volume 180, Issue 1, pp. 39–48 [ arXiv ] [ Journal Link ]. [ERC] [DOI]


Geometric Group Theory and its Applications in Geometric Topology

  1. Random Groups at Density d<1/2: Sharp Length Inequalities for Generalized Torsion and a Fixed-width Exclusion via First-order Transfer, to appear in Arch. Math. arXiv:2602.02183. [NRF25]

  2. On the kernel of actions on asymptotic cones (with W. Jang), J. Group Theory., vol. 28, no. 4, 2025, pp. 753-809. [ arXiv ], [ Journal Link ] . [NRF20] [DOI]

  3. Linear growth of translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces (with I. Choi, D. M. Kim), J. Inst. Math. Jussieu, Volume 23 , Issue 4 , 2024 , pp. 1751 - 1795 [ arXiv ], [ Journal Link ]. [Samsung]

  4. On the finiteness property of hyperbolic simplicial actions: the right-angled Artin groups and their extension graphs (with D. Seo, H. Shin), Geom. Dedicata. 217, 7 (2023) [ arXiv ], [ Journal Link ]. [NRF20] [DOI]

  5. Subgroup growth of right-angled Artin and Coxeter groups (with B. Petri, J. Raimbault), J. Lond. Math. Soc. (2020) Vol 101, Issue 2, pp. 556-588. [ arXiv ], [ Journal Link ]. [Samsung] [DOI]

  6. Subgroup growth of virtually cyclic right-angled Coxeter groups and their free products (with B. Petri, J. Raimbault), Combinatorica (2019), 39 (4), pp. 779–811. [ arXiv ], [ Journal Link ]. [Samsung] [DOI]

  7. Unsmoothable group actions on compact one-manifolds (with S. Kim and T. Koberda), J. Eur. Math. Soc. (2019), Volume 21, Issue 8, pp. 2333-2353. [ arXiv ], [ Journal Link ]. [ERC] [DOI]

  8. On laminar groups, Tits alternatives and convergence group actions on S² (with J. Alonso, E. Samperton), J. Group Theory (2019), Volume 22, Issue 3, pp. 359-381. [ arXiv ], [ Journal Link ]. [ERC/Samsung] [DOI]

  9. Spaces of invariant circular orders of groups (with E. Samperton), Groups Geom. Dyn. (2018), Volume 12, Issue 2, 2018, pp. 721–763 [ arXiv ], [ Journal Link ]. [ERC] [DOI]

  10. Right-angled Artin groups in the C∞ diffeomorphism group of the real line (with S. Kim and T. Koberda), Israel J. Math. (2016), Volume 213, Issue 1, pp. 175–182. [ arXiv ] [ Journal Link ]. [DOI]

  11. Fuchsian Groups, Circularly Ordered Groups, and Dense Invariant Laminations on the Circle, Geom. Topol. 19-4 (2015), 2081-2115. [ arXiv ] [ Journal Link ]. [DOI]


Other topics in Geometric Topology and related areas  

  1. Monodromy through narrow bifurcation locus of the Mandelbrot set (with J. Baik), Glasnik Matematicki (2026), 61(1), pp. 77–115. [ arXiv ] [ Journal Link ]. [NRF20] [DOI]

  2. Degree-d-invariant laminations (with William P. Thurston, Yan Gao, John H. Hubbard, Tan Lei, Kathryn A. Lindsey, Dylan P. Thurston), What's Next?: The Mathematical Legacy of William P. Thurston (Annals of Mathematics Studies 205) (2020), pp. 259–325. [ arXiv ], [ Book Link ]. [Samsung] [DOI]

  3. Limits of canonical forms on towers of Riemann surfaces (with F. Shokrieh, C. Wu), J. Reine Angew. Math (Crelle's journal) (2020), Volume 2020, Issue 764, Pages 287–304. [ arXiv ], [ Journal Link ]. [Samsung] [DOI]

  4. An algorithm to compute the Teichmüller polynomial from matrices (with C. Wu, K. Kim, T. Jo), Geom. Dedicata. (2020) Vol 204, pp. 175–189. [ arXiv ], [ Journal Link ]. [ERC] [DOI]

  5. The Space of Geometric Limits of Abelian Subgroups of PSL(2,C) (with L. Clavier), Hiroshima Math. J. (2016), Volume 46, Number 1, 1-36. [ arXiv ] [ Journal Link ]. [DOI]

  6. The Space of Geometric Limits of One-generator Closed Subgroups of PSL(2, R) (with L. Clavier), Algebr. Geom. Topol., Vol 13, Issue 1 (2013), pp. 549-576. [ arXiv ] [ Journal Link ] [DOI]


Applied Math / AI for Math

  1. SH²: A Mathematician-Curated benchmark for Assessing Research-level Math Capabilities of LLMs (with Guijin Son et al.), accepted at NeurIPS 2026, Evaluations & Datasets Track (poster). Preprint title: Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs. arXiv:2605.09063 .

  2. TopoCL: Topological Contrastive Learning for Time Series (With N. Kim, Y. Yoon), IEEE Transactions on Neural Networks and Learning Systems 37(9) (2026), pp. 4863–4874. 10.1109/TNNLS.2026.3675422. [ arXiv ], [ Journal Link ]. [DOI]

  3. Genomic GPS: using genetic distance from individuals to public data for genomic analysis without disclosing personal genomes (with K. Kim, C. S. Jang, J. Roh, E. Eskin, B. Han), Genome Biology, volume 20, Article number: 175 (2019) [ Journal Link ]. [DOI]



Preprints (draft is available either on arXiv or via a link below)  

  1. Lean-GAP: A Dataset of Formalized Graduate Algebra Problems (with Seewoo Lee et al.), arXiv:2606.02588 . [NRF25]

  2. Co-Hopfianity is not a profinite property (with W. Jang), arXiv:2603.04197 . [NRF25]

  3. Uniform Perfectness and Centers in Sublinearly Morse Boundaries, arXiv:2602.14673 . [NRF25]

  4. Optimizing the Upper-Bound Constant for the Crossing Number of Polynomial Curve Systems, arXiv:2602.02144 . [NRF25]

  5. Reconstruction of Anosov flows from infinity (with C. Wu, B. Zhao), arXiv:2407.07634 . [NRF25]

  6. Acylindrical hyperbolicity of outer automorphism groups of right-angled Artin groups (with J. Kim), arXiv:2405.19702 . [NRF20]



PhD Thesis 

Other writings  

  • Introduction to Chabauty topology and Pictures of the Chabauty space of C^* (with L. Clavier), arXiv:1209.0221. [arXiv]

  • Two articles in the book Encyclopedia of Mathematics and Society : Geometry in Society (pp. 427-433), and Measurements, Volume (pp. 651-653), Salem Press (2011).

  • One chapter in the book Handbook of the Mathematics of the Arts and Sciences: Almost all surfaces are made out of hexagons , Springer (2021), pp. 169–174. [DOI]