Research

Papers, talks, and activities

Published papers

Most papers can be downloaded at http://arxiv.org/a/kim_s_3

35. Inhyeok Choi, Sang-hyun Kim, Smoothing countable group actions on metrizable spaces, to appear in Advanced Studies in Pure Mathematics (Proceedings of Mathematical Society of Japan - Seasonal Institute).
[Summary]

Every topological action of a countable group on a metrizable space can be promoted to a bi-Lipschitz action with respect to a suitably chosen compatible metric. The same conclusion holds for closed subgroups of locally compact groups. This generalizes earlier work of Hamenstädt on finitely generated groups, and recovers a smoothing theorem of Deroin, Kleptsyn, and Navas for actions on one-manifolds.

[Arxiv]
[cite]
```
@misc{arxiv:2410.06077,
      title={Smoothing countable group actions on metrizable spaces}, 
      author={Inhyeok Choi and Sang-hyun Kim},
      year={2026},
      eprint={2410.06077},
      archivePrefix={arXiv},
      primaryClass={math.GR},
      url={https://arxiv.org/abs/2410.06077}
}
```
34. Sang-hyun Kim, Nicolás Matte Bon, Mikael de la Salle and Michele Triestino, Subexponential growth and C¹ actions on one-manifolds, International Mathematics Research Notices, Volume 2025, Issue 13, July 2025, rnaf202.
[Summary]

For countable groups without finitely generated subgroups of exponential growth, every faithful topological action on a compact connected one-manifold can be blown up to a C¹ action. The proof relies on a combinatorial characterization of such groups and extends techniques from smooth dynamics. This identifies a precise algebraic condition under which topological rigidity can be upgraded to differentiable regularity.

[Journal] [Arxiv]
[cite]
```
@article {MR4929825,
    AUTHOR = {Kim, Sang-hyun and de la Salle, Mikael and Matte Bon,
              Nicol\'{a}s and Triestino, Michele},
     TITLE = {Subexponential growth and {$\rm C^1$} actions on
              one-manifolds},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2025},
    NUMBER = {13},
     PAGES = {Paper No. rnaf202, 12},
      ISSN = {1073-7928,1687-0247},
   MRCLASS = {57M60},
  MRNUMBER = {4929825},
MRREVIEWER = {Sanghoon\ Kwon},
       DOI = {10.1093/imrn/rnaf202},
       URL = {https://doi.org/10.1093/imrn/rnaf202},
}
```
33. Sang-hyun Kim, Thomas Koberda and Javier de la Nuez-Gonzalez. First order rigidity of homeomorphism groups of manifolds, Comm. Amer. Math. Soc. 5 (2025), 144-194.
[Summary]

A compact connected manifold of dimension at least two is uniquely determined, up to homeomorphism, by a single first-order sentence in the language of groups evaluated on its homeomorphism group. In particular, the first-order theory of the homeomorphism group is a complete invariant of the underlying manifold. Analogous rigidity results are established for measure-preserving homeomorphism groups and diffeomorphism groups, forging a direct link between the model theory of transformation groups and the topology of manifolds.

[Journal] [Arxiv]
[cite]
```
@article {MR4904300,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas and de la Nuez
              Gonz\'{a}lez, J.},
     TITLE = {First order rigidity of homeomorphism groups of manifolds},
   JOURNAL = {Commun. Am. Math. Soc.},
  FJOURNAL = {Communications of the American Mathematical Society},
    VOLUME = {5},
      YEAR = {2025},
     PAGES = {144--194},
      ISSN = {2692-3688},
   MRCLASS = {03C07 (20A15 57M60 57S05 57S25)},
  MRNUMBER = {4904300},
       DOI = {10.1090/cams/47},
       URL = {https://doi.org/10.1090/cams/47},
}
```
32. Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang, Ser Peow Tan. Optimal independent generating system for the congruence subgroups Γ₀(p) and Γ₀(pq), The Journal of Geometric Analysis (2025) 35:216.
[Summary]

For primes p and distinct primes p, q, an explicit independent generating system for the congruence subgroups Γ₀(p) and Γ₀(pq) of SL(2,ℤ) is constructed, where each generator has its (2,1)-entry equal to n or 0. This resolves a conjecture of Kulkarni for these subgroups. The proof is geometric, based on the action of Γ₀(n) on the Farey graph in the hyperbolic plane and the combinatorics of the resulting quotient.

[Journal] [Arxiv]
[cite]
```
@article {MR4917150,
    AUTHOR = {Doan, Nhat Minh and Kim, Sang-hyun and Lang, Mong Lung and
              Tan, Ser Peow},
     TITLE = {Optimal special polygons for the congruence subgroups {$\Gamma
              _0(p)$} and {$\Gamma _0(pq)$}},
   JOURNAL = {J. Geom. Anal.},
  FJOURNAL = {Journal of Geometric Analysis},
    VOLUME = {35},
      YEAR = {2025},
    NUMBER = {7},
     PAGES = {Paper No. 216, 28},
      ISSN = {1050-6926,1559-002X},
   MRCLASS = {11F06 (11B57 30F35)},
  MRNUMBER = {4917150},
MRREVIEWER = {Michelle\ Chu},
       DOI = {10.1007/s12220-025-02051-y},
       URL = {https://doi.org/10.1007/s12220-025-02051-y},
}
```
31. Sang-hyun Kim and Thomas Koberda. Non-freeness of groups generated by two parabolic elements with small rational parameters. Michigan Mathematical Journal (2022).
[Summary]

Given two parabolic elements in SL(2,ℂ) parameterized by a rational number s/r, the group they generate is shown to be non-free for all numerators s ≤ 27 (with a partial exception at s = 24). For larger numerators, density estimates are provided. The proofs combine algebraic arguments with computer-assisted verification, contributing to the broader question of when two-generator subgroups of SL(2,ℂ) fail to be free.

[Journal] [Arxiv]
[cite]
```
@article {MR4505367,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas},
     TITLE = {Non-freeness of groups generated by two parabolic elements
              with small rational parameters},
   JOURNAL = {Michigan Math. J.},
  FJOURNAL = {Michigan Mathematical Journal},
    VOLUME = {71},
      YEAR = {2022},
    NUMBER = {4},
     PAGES = {809--833},
      ISSN = {0026-2285,1945-2365},
   MRCLASS = {20H10 (20-08 20F05)},
  MRNUMBER = {4505367},
MRREVIEWER = {Jack\ O.\ Button},
       DOI = {10.1307/mmj/20205868},
       URL = {https://doi.org/10.1307/mmj/20205868},
}
```
30. Sang-hyun Kim and Genevieve Walsh. Some groups with planar boundaries, Surveys in Differential Geometry (2022).
[Summary]

This survey illustrates Bowditch's canonical JSJ splitting of one-ended hyperbolic groups, with emphasis on how planarity of the Gromov boundary constrains the algebraic structure of the group. A central theme is the Kapovich–Kleiner conjecture, which predicts that a one-ended hyperbolic group with planar boundary acts geometrically on a 3-manifold with boundary.

[Journal] [Arxiv]
[cite]
```
@incollection {MR4479754,
    AUTHOR = {Kim, Sang-hyun and Walsh, Genevieve},
     TITLE = {Some groups with planar boundaries},
 BOOKTITLE = {Surveys in differential geometry 2020. {S}urveys in 3-manifold
              topology and geometry},
    SERIES = {Surv. Differ. Geom.},
    VOLUME = {25},
     PAGES = {253--280},
 PUBLISHER = {Int. Press, Boston, MA},
      YEAR = {[2022] \copyright 2022},
      ISBN = {978-1-57146-419-4},
   MRCLASS = {20F67 (20F65 57Sxx)},
  MRNUMBER = {4479754},
}
```
29. Sang-hyun Kim, Thomas Koberda and Cristóbal Rivas. Virtual critical regularity of mapping class group actions on the circle, Transformation Groups (2022).
[Summary]

The free product (G × H) ∗ ℤ, where G and H are non-solvable, admits no embedding into the group of orientation-preserving C^{1+τ} diffeomorphisms of the circle for any τ > 0. As a consequence, no finite-index subgroup of the mapping class group of a closed surface of genus at least two can act faithfully on the circle by C^{1+τ} diffeomorphisms. This pins down the virtual critical regularity of mapping class group actions at exactly C¹.

[Journal] [Arxiv]
[cite]
```
@article {MR4788024,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas and Rivas, Crist\'{o}bal},
     TITLE = {Virtual critical regularity of mapping class group actions on
              the circle},
   JOURNAL = {Transform. Groups},
  FJOURNAL = {Transformation Groups},
    VOLUME = {29},
      YEAR = {2024},
    NUMBER = {3},
     PAGES = {1105--1114},
      ISSN = {1083-4362,1531-586X},
   MRCLASS = {57M60 (20F14 20F36 37C05 37C85 57K20)},
  MRNUMBER = {4788024},
MRREVIEWER = {Marja\ K.\ Kankaanrinta},
       DOI = {10.1007/s00031-022-09698-9},
       URL = {https://doi.org/10.1007/s00031-022-09698-9},
}
```
28. Sang-hyun Kim and Thomas Koberda. Structure and regularity of group actions on one-manifolds, Springer Monographs in Mathematics (2021).
[Summary]

This monograph presents a systematic study of the interplay between algebraic structure of groups and their actions on one-manifolds by diffeomorphisms of varying regularity. The theory of critical regularity is developed, showing how the optimal smoothness of a group action is determined by algebraic constraints such as the presence of direct products or free products. Key topics include right-angled Artin group actions, mapping class group dynamics, and phenomena related to Denjoy's theorem, bringing together classical results and recent developments at the interface of geometric group theory and smooth dynamics.

[Journal] [Arxiv]
[cite]
```
@book {MR4381312,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas},
     TITLE = {Structure and regularity of group actions on one-manifolds},
    SERIES = {Springer Monographs in Mathematics},
 PUBLISHER = {Springer, Cham},
      YEAR = {[2021] \copyright 2021},
     PAGES = {xiv+323},
      ISBN = {978-3-030-89005-6; 978-3-030-89006-3},
   MRCLASS = {57M60 (20F65 37C85)},
  MRNUMBER = {4381312},
       DOI = {10.1007/978-3-030-89006-3},
       URL = {https://doi.org/10.1007/978-3-030-89006-3},
}
```
27. Sang-hyun Kim, Thomas Koberda and Cristóbal Rivas. Direct products, overlapping actions, and critical regularity, Journal of Modern Dynamics, Vol. 17 (June 2021), pp. 285-304.
[Summary]

The free product (G × H) ∗ ℤ, where G and H are non-solvable, does not embed into the group of orientation-preserving C^{1+τ} diffeomorphisms of a compact interval for any τ > 0. The proof introduces the technique of analyzing "overlapping" actions of direct product subgroups to detect regularity obstructions. This provides a counterpart on the interval to parallel results on the circle, further constraining how algebraic complexity limits differentiable regularity.

[Journal] [Arxiv]
[cite]
```
@article {MR4288175,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas and Rivas, Crist\'{o}bal},
     TITLE = {Direct products, overlapping actions, and critical regularity},
   JOURNAL = {J. Mod. Dyn.},
  FJOURNAL = {Journal of Modern Dynamics},
    VOLUME = {17},
      YEAR = {2021},
     PAGES = {285--304},
      ISSN = {1930-5311,1930-532X},
   MRCLASS = {57M60 (20F14 20F36 20F60 37C85 37E05)},
  MRNUMBER = {4288175},
MRREVIEWER = {Andrzej\ W.\ Bi\'{s}},
       DOI = {10.3934/jmd.2021009},
       URL = {https://doi.org/10.3934/jmd.2021009},
}
```

26. Sang-hyun Kim, Thomas Koberda, Jaejeong Lee, Ken'ichi Ohshika and Ser Peow Tan; appendix by Xinghua Gao. Shapes of hyperbolic triangles and once-punctured torus groups, Mathematische Zeitschrift (2021).

[Summary]

The paper studies the moduli of once-punctured torus groups parameterized by the shape of a hyperbolic ideal triangle. For irrational cone angles, the precise regions in parameter space where the monodromy representation yields a free group are determined. The analysis uses continued fraction expansions and the combinatorics of the Farey graph to detect when discreteness and faithfulness hold.

[Journal] [Arxiv]

[cite]

@article {MR4329281,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas and Lee, Jaejeong and
              Ohshika, Ken'ichi and Tan, Ser Peow and Gao, Xinghua},
     TITLE = {Shapes of hyperbolic triangles and once-punctured torus
              groups},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {299},
      YEAR = {2021},
    NUMBER = {3-4},
     PAGES = {2103--2130},
      ISSN = {0025-5874,1432-1823},
   MRCLASS = {30F35 (11J70 20E05 20H10 30F40)},
  MRNUMBER = {4329281},
MRREVIEWER = {Michelle\ Chu},
       DOI = {10.1007/s00209-021-02745-3},
       URL = {https://doi.org/10.1007/s00209-021-02745-3},
}

25. Sang-hyun Kim and Thomas Koberda. Integrability of moduli and regularity of Denjoy counterexamples. Discrete and Continuous Dynamical Systems-A, October 2020, 40(10): 6061-6088.
[Summary]

For a concave modulus of continuity α whose reciprocal is integrable near zero, there exists a C^{1,α} diffeomorphism of the circle possessing an exceptional minimal set (a Cantor set). This result extends to actions of groups with polynomial growth, giving a near-optimal condition for constructing Denjoy-type counterexamples. A partial converse is also established, delineating the threshold between smooth rigidity and the existence of exceptional minimal sets.

[Journal] [Arxiv]
[cite]
```
@article {MR4128339,
    AUTHOR = {Kim, Sang-Hyun and Koberda, Thomas},
     TITLE = {Integrability of moduli and regularity of {D}enjoy
              counterexamples},
   JOURNAL = {Discrete Contin. Dyn. Syst.},
  FJOURNAL = {Discrete and Continuous Dynamical Systems},
    VOLUME = {40},
      YEAR = {2020},
    NUMBER = {10},
     PAGES = {6061--6088},
      ISSN = {1078-0947,1553-5231},
   MRCLASS = {37E10 (37C05 37C15 37C85 37E45)},
  MRNUMBER = {4128339},
MRREVIEWER = {Puneet\ Sharma},
       DOI = {10.3934/dcds.2020259},
       URL = {https://doi.org/10.3934/dcds.2020259},
}
```
24. Christian Bonatti, Sang-hyun Kim, Thomas Koberda and Michele Triestino. Small C¹ actions of semidirect products on compact manifolds, Algebraic & Geometric Topology 20 (2020) 3183–3203.
[Summary]

For a finitely generated semidirect product G = H ⋋ ⟨t⟩ whose conjugation action on the first cohomology of H is hyperbolic, every C¹ action on a compact manifold sufficiently close to the trivial action factors through an abelian group. This applies, for instance, to fundamental groups of fibered hyperbolic 3-manifolds. The result reveals that local rigidity phenomena for smooth group actions are controlled by the spectral properties of the monodromy.

[Journal] [Arxiv]
[cite]
```
@article {MR4185939,
    AUTHOR = {Bonatti, Christian and Kim, Sang-hyun and Koberda, Thomas and
              Triestino, Michele},
     TITLE = {Small {$C^1$} actions of semidirect products on compact
              manifolds},
   JOURNAL = {Algebr. Geom. Topol.},
  FJOURNAL = {Algebraic \& Geometric Topology},
    VOLUME = {20},
      YEAR = {2020},
    NUMBER = {6},
     PAGES = {3183--3203},
      ISSN = {1472-2747,1472-2739},
   MRCLASS = {37C85 (20E22 37D30 57M50 57M60 57R35)},
  MRNUMBER = {4185939},
MRREVIEWER = {Shigenori\ Matsumoto},
       DOI = {10.2140/agt.2020.20.3183},
       URL = {https://doi.org/10.2140/agt.2020.20.3183},
}
```
23. Sang-hyun Kim and Thomas Koberda. Diffeomorphism groups of critical regularity. Inventiones mathematicae, 221(2), 421-501 (2020).
[Summary]

For each real number α ≥ 1, finitely generated groups are constructed that embed into the group of C^α diffeomorphisms of the circle but admit no embedding at any higher regularity. Complementary groups are also built that embed at every regularity below α but not at α itself. These groups, and their commutator subgroups (which are simple), witness the fact that the regularity spectrum of diffeomorphism groups is fully realized, confirming that critical regularity is a genuine and sharp phenomenon.

[Journal] [Arxiv]
[cite]
```
@article {MR4121156,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas},
     TITLE = {Diffeomorphism groups of critical regularity},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {221},
      YEAR = {2020},
    NUMBER = {2},
     PAGES = {421--501},
      ISSN = {0020-9910,1432-1297},
   MRCLASS = {57M60 (20F36 37C05 37C85 57S05)},
  MRNUMBER = {4121156},
MRREVIEWER = {Shigenori\ Matsumoto},
       DOI = {10.1007/s00222-020-00953-y},
       URL = {https://doi.org/10.1007/s00222-020-00953-y},
}
```
22. Sang-hyun Kim, Thomas Koberda and Mahan Mj, Flexibility of Group Actions on the Circle, Springer Lecture Notes in Mathematics 2231 (2019).
[Summary]

The paper characterizes finitely generated groups admitting uncountably many pairwise non-conjugate faithful representations into PSL(2,ℝ). A combination theorem for such groups is established, encompassing free products and HNN extensions amalgamated over maximal cyclic subgroups. This shows that flexibility of circle actions, in the sense of having a large moduli space of representations, is widespread among groups acting on the circle.

[Journal] [Arxiv]
[cite]
```
@book {MR3887602,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas and Mj, Mahan},
     TITLE = {Flexibility of group actions on the circle},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {2231},
 PUBLISHER = {Springer, Cham},
      YEAR = {2019},
     PAGES = {x+134},
      ISBN = {978-3-030-02854-1; 978-3-030-02855-8},
   MRCLASS = {37-02 (20F34 20F65 37C85 37D40 37F30 57M60)},
  MRNUMBER = {3887602},
MRREVIEWER = {Jo\~{a}o\ Paulo\ Almeida},
       DOI = {10.1007/978-3-030-02855-8},
       URL = {https://doi.org/10.1007/978-3-030-02855-8},
}
```
21. Sang-hyun Kim, Thomas Koberda and Yash Lodha, Chain groups of homeomorphisms of the interval and the circle, Annales Scientifiques de l'École Normale Supérieure, Series 4, Volume (52), 2019, 797-820.
[Summary]

Subgroups of the homeomorphism group of the real line generated by finitely many homeomorphisms, each supported on a single bounded interval, are studied systematically. The group-theoretic structure of these "chain groups" is determined: they are characterized in terms of simplicity, finite generation, and left-orderability. As the main application, uncountably many pairwise non-isomorphic finitely generated simple left-orderable groups are constructed.

[Journal] [Arxiv]
[cite]
```
@article {MR4038452,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas and Lodha, Yash},
     TITLE = {Chain groups of homeomorphisms of the interval},
   JOURNAL = {Ann. Sci. \'{E}c. Norm. Sup\'{e}r. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure.
              Quatri\`eme S\'{e}rie},
    VOLUME = {52},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {797--820},
      ISSN = {0012-9593,1873-2151},
   MRCLASS = {57S05 (20F65 37C85)},
  MRNUMBER = {4038452},
MRREVIEWER = {Michele\ Triestino},
       DOI = {10.24033/asens.2397},
       URL = {https://doi.org/10.24033/asens.2397},
}
```
20. Hyungryul Baik, Sang-hyun Kim and Thomas Koberda. Unsmoothable group actions on compact one-manifolds, Journal of European Mathematical Society, Volume 21, Issue 8, 2019, pp. 2333–2353.
[Summary]

Mapping class groups of surfaces that are not virtually free admit no faithful C^{1+bv} actions on the circle, even after passing to finite-index subgroups. The proof exploits algebraic constraints arising from Dehn twist relations in the mapping class group. This establishes that the topological actions of mapping class groups on the circle are inherently unsmoothable beyond Lipschitz regularity.

[Journal] [Arxiv]
[cite]
```
@article {MR4035847,
    AUTHOR = {Baik, Hyungryul and Kim, Sang-hyun and Koberda, Thomas},
     TITLE = {Unsmoothable group actions on compact one-manifolds},
   JOURNAL = {J. Eur. Math. Soc. (JEMS)},
  FJOURNAL = {Journal of the European Mathematical Society (JEMS)},
    VOLUME = {21},
      YEAR = {2019},
    NUMBER = {8},
     PAGES = {2333--2353},
      ISSN = {1435-9855,1435-9863},
   MRCLASS = {20F36 (20F65 37E10 57M60)},
  MRNUMBER = {4035847},
MRREVIEWER = {Jens\ Harlander},
       DOI = {10.4171/jems/886},
       URL = {https://doi.org/10.4171/jems/886},
}
```
19. Sang-hyun Kim and Thomas Koberda. Free products and algebraic structures of diffeomorphism groups, Journal of Topology, Volume 11, Issue 4, December 2018, Pages 1053-1075.
[Summary]

If a finitely generated group G is not virtually abelian, then the free product (G × ℤ) ∗ ℤ does not embed into the C^{1+bv} diffeomorphism group of a compact one-manifold. This yields a complete classification of right-angled Artin groups that embed into the diffeomorphism group of the circle at each regularity 0 ≤ r ≤ ω, extending earlier results that covered only the cases r ≤ 1 and r = ω.

[Journal] [Arxiv]
[cite]
```
@article {MR3989437,
    AUTHOR = {Kim, Sang-Hyun and Koberda, Thomas},
     TITLE = {Free products and the algebraic structure of diffeomorphism
              groups},
   JOURNAL = {J. Topol.},
  FJOURNAL = {Journal of Topology},
    VOLUME = {11},
      YEAR = {2018},
    NUMBER = {4},
     PAGES = {1054--1076},
      ISSN = {1753-8416,1753-8424},
   MRCLASS = {57M60 (20F36 37C05 37C85 57S05)},
  MRNUMBER = {3989437},
MRREVIEWER = {Ji-Young\ Ham},
       DOI = {10.1112/topo.12079},
       URL = {https://doi.org/10.1112/topo.12079},
}
```
18. Sang-hyun Kim. Surface subgroups of word-hyperbolic groups (survey), Handbook of group actions. Vol. III, 89-102.
[Summary]

This survey examines Gromov's question of whether every one-ended word-hyperbolic group contains a surface subgroup. Known positive results are collected, including cases arising from doubles of free groups and groups acting on CAT(0) cube complexes. The connections to Cannon's conjecture and the structure of hyperbolic group boundaries are also discussed.
[cite]
```
@incollection {MR3888617,
    AUTHOR = {Kim, Sang-hyun},
     TITLE = {Surface subgroups of word-hyperbolic groups},
 BOOKTITLE = {Handbook of group actions. {V}ol. {III}},
    SERIES = {Adv. Lect. Math. (ALM)},
    VOLUME = {40},
     PAGES = {87--100},
 PUBLISHER = {Int. Press, Somerville, MA},
      YEAR = {2018},
      ISBN = {978-1-57146-364-7},
   MRCLASS = {20F36 (05C25 20F65)},
  MRNUMBER = {3888617},
MRREVIEWER = {Jordi\ Delgado},
}
```

17. Sang-hyun Kim and Thomas Koberda. RAAGs in Diffeos (survey), Advanced Studies in Pure Mathematics: Volume 73, 215-224 (2017).

[Summary]

This survey article describes embeddings of right-angled Artin groups (RAAGs) into diffeomorphism groups of manifolds. The interplay between the defining graph of a RAAG and the regularity of the resulting diffeomorphism action is discussed, highlighting how combinatorial graph-theoretic properties translate into dynamical constraints.

[Journal] [Arxiv]

[cite]

@incollection {MR3728499,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas},
     TITLE = {R{AAG}s in diffeos},
 BOOKTITLE = {Hyperbolic geometry and geometric group theory},
    SERIES = {Adv. Stud. Pure Math.},
    VOLUME = {73},
     PAGES = {215--224},
 PUBLISHER = {Math. Soc. Japan, Tokyo},
      YEAR = {2017},
      ISBN = {978-4-86497-042-6},
   MRCLASS = {20F36 (57M60)},
  MRNUMBER = {3728499},
MRREVIEWER = {Mustafa\ Korkmaz},
       DOI = {10.2969/aspm/07310215},
       URL = {https://doi.org/10.2969/aspm/07310215},
}

16. Cheol-Hyun Cho, Hansol Hong, Sang-hyun Kim and Siu-Cheong Lau. Lagrangian Floer potential of orbifold spheres, Advances in Mathematics, Volume 306, 14 January 2017, Pages 344-426.
[Summary]

Lagrangian Floer potentials are computed for Seidel Lagrangians on hyperbolic 2-orbifold spheres—orbifold projective lines with three orbifold points and negative orbifold Euler characteristic. The computation involves counting pseudo-holomorphic polygon contributions within the framework of A-infinity categories. This provides explicit formulas connecting Lagrangian Floer theory to the geometry of orbifold surfaces.

[Journal] [Arxiv]
[cite]
```
@article {MR3581306,
    AUTHOR = {Cho, Cheol-Hyun and Hong, Hansol and Kim, Sang-hyun and Lau,
              Siu-Cheong},
     TITLE = {Lagrangian {F}loer potential of orbifold spheres},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {306},
      YEAR = {2017},
     PAGES = {344--426},
      ISSN = {0001-8708,1090-2082},
   MRCLASS = {14N35 (14J33)},
  MRNUMBER = {3581306},
MRREVIEWER = {Guangbo\ Xu},
       DOI = {10.1016/j.aim.2016.10.017},
       URL = {https://doi.org/10.1016/j.aim.2016.10.017},
}
```

15. Hyungryul Baik, Sang-hyun Kim and Thomas Koberda. Right-angled Artin groups in the C^∞ diffeomorphism group of the real line, Israel Journal of Mathematics, June 2016, Volume 213, Issue 1, pp 175-182.

[Summary]

Every right-angled Artin group (RAAG) is shown to embed into the group of C∞ diffeomorphisms of the real line. The proof constructs explicit smooth bump functions that realize the required group action. This settles the embeddability question for RAAGs into smooth diffeomorphism groups in the non-compact setting.

[Journal] [Arxiv]

[cite]

@article {MR3509472,
     AUTHOR = {Baik, Hyungryul and Kim, Sang-hyun and Koberda, Thomas},
      TITLE = {Right-angled {A}rtin groups in the {$C^\infty$} diffeomorphism
               group of the real line},
    JOURNAL = {Israel J. Math.},
   FJOURNAL = {Israel Journal of Mathematics},
     VOLUME = {213},
       YEAR = {2016},
     NUMBER = {1},
      PAGES = {175--182},
       ISSN = {0021-2172,1565-8511},
    MRCLASS = {20F36 (03D35 20E26 58D05)},
   MRNUMBER = {3509472},
 MRREVIEWER = {Valeriy\ G.\ Bardakov},
        DOI = {10.1007/s11856-016-1307-8},
        URL = {https://doi.org/10.1007/s11856-016-1307-8},
}

14. Sang-hyun Kim and Thomas Koberda. Right-angled Artin groups and finite subgraphs of curve graphs, Osaka Journal of Mathematics, Volume 53, Number 3 (2016), 705-716.
[Summary]

For surfaces S with complexity ξ(S) < 3, a RAAG A(Γ) embeds into the mapping class group Mod(S) only if Γ appears as an induced subgraph of the curve graph C(S). For surfaces of higher complexity, explicit counterexamples show that this criterion fails. The result clarifies the extent to which the combinatorics of the curve graph governs RAAG embeddings into mapping class groups.

[Journal] [Arxiv]
[cite]
```
@article {MR3533464,
     AUTHOR = {Kim, Sang-Hyun and Koberda, Thomas},
      TITLE = {Right-angled {A}rtin groups and finite subgraphs of curve
               graphs},
    JOURNAL = {Osaka J. Math.},
   FJOURNAL = {Osaka Journal of Mathematics},
     VOLUME = {53},
       YEAR = {2016},
     NUMBER = {3},
      PAGES = {705--716},
       ISSN = {0030-6126},
    MRCLASS = {20F36 (20F34 20F65 57M15)},
   MRNUMBER = {3533464},
 MRREVIEWER = {Daniel\ Matei},
        URL = {http://projecteuclid.org/euclid.ojm/1470413985},
}
```

13. Sang-hyun Kim and Thomas Koberda. Anti-trees and right-angled Artin subgroups of braid groups, Geometry & Topology 19-6 (2015), 3289–3306.

[Summary]

Every RAAG embeds into a RAAG whose defining graph is an anti-tree. Since anti-tree RAAGs are known to embed into braid groups, it follows that every RAAG embeds into some braid group. As a further consequence, every RAAG embeds quasi-isometrically into the area-preserving diffeomorphism group of the 2-sphere with respect to the L^p metric for p > 2.

[Journal] [Arxiv]

[cite]

@article {MR3447104,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas},
     TITLE = {Anti-trees and right-angled {A}rtin subgroups of braid groups},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {19},
      YEAR = {2015},
    NUMBER = {6},
     PAGES = {3289--3306},
      ISSN = {1465-3060,1364-0380},
   MRCLASS = {20F36 (03D35 20F10 20F67 57M07)},
  MRNUMBER = {3447104},
MRREVIEWER = {Volker\ Gebhardt},
       DOI = {10.2140/gt.2015.19.3289},
       URL = {https://doi.org/10.2140/gt.2015.19.3289},
}

12. Sang-hyun Kim and Genevieve Walsh. Coxeter groups, hyperbolic cubes, and acute triangulations, Journal of Topology (2016) 9 (1): 117-142.
[Summary]

A combinatorial triangulation of the 2-sphere can be realized as an acute geodesic triangulation if and only if it contains no separating 3- or 4-cycle. The proof leverages the theory of hyperbolic Coxeter groups and the geometry of right-angled polytopes in hyperbolic space. This gives a complete combinatorial characterization of acute triangulability for the sphere.

[Journal] [Arxiv]
[cite]
```
@article {MR3465843,
    AUTHOR = {Kim, S.-h. and Walsh, G. S.},
     TITLE = {Coxeter groups, hyperbolic cubes and acute triangulations},
   JOURNAL = {J. Topol.},
  FJOURNAL = {Journal of Topology},
    VOLUME = {9},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {117--142},
      ISSN = {1753-8416,1753-8424},
   MRCLASS = {57M07 (20F65)},
  MRNUMBER = {3465843},
MRREVIEWER = {Bruno\ P.\ Zimmermann},
       DOI = {10.1112/jtopol/jtv038},
       URL = {https://doi.org/10.1112/jtopol/jtv038},
}
```
11. Sang-hyun Kim and Thomas Koberda. The geometry of the curve complex of a right-angled Artin group, International Journal of Algebra and Computation (2014) 24 (2) 121-169.
[Summary]

A theory of right-angled Artin group actions on their extension graphs is developed, paralleling the classical theory of mapping class group actions on curve graphs. In particular, these actions are shown to be acylindrical, and explicit acylindricity constants are computed. The framework establishes extension graphs as a natural geometric tool for studying the internal structure and quasi-isometric rigidity of RAAGs.

[Journal] [Arxiv]
[cite]
```
@article {MR3192368,
    AUTHOR = {Kim, Sang-Hyun and Koberda, Thomas},
     TITLE = {The geometry of the curve graph of a right-angled {A}rtin
              group},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {24},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {121--169},
      ISSN = {0218-1967,1793-6500},
   MRCLASS = {20F36 (05E45)},
  MRNUMBER = {3192368},
MRREVIEWER = {Thomas\ Haettel},
       DOI = {10.1142/S021819671450009X},
       URL = {https://doi.org/10.1142/S021819671450009X},
}
```
10. Sang-hyun Kim and Sang-il Oum. Hyperbolic Surface subgroups of one-ended doubles of free groups, Journal of Topology (2014) 7 (4): 927–947.
[Summary]

The double of a rank-two free group along a one-ended amalgamation is shown to either split as a nontrivial free product or contain a closed hyperbolic surface subgroup. This provides evidence for Gromov's conjecture that every one-ended word-hyperbolic group contains a surface subgroup. The proof uses a combination of combinatorial group theory and the geometry of van Kampen diagrams.

[Journal] [Arxiv]
[cite]
```
@article {MR3286893,
    AUTHOR = {Kim, Sang-hyun and Oum, Sang-il},
     TITLE = {Hyperbolic surface subgroups of one-ended doubles of free
              groups},
   JOURNAL = {J. Topol.},
  FJOURNAL = {Journal of Topology},
    VOLUME = {7},
      YEAR = {2014},
    NUMBER = {4},
     PAGES = {927--947},
      ISSN = {1753-8416,1753-8424},
   MRCLASS = {20F65 (05C70 57M20)},
  MRNUMBER = {3286893},
MRREVIEWER = {David\ Hume},
       DOI = {10.1112/jtopol/jtu004},
       URL = {https://doi.org/10.1112/jtopol/jtu004},
}
```
9. Sang-hyun Kim and Thomas Koberda. An obstruction to embedding right-angled Artin groups in mapping class groups, International Mathematics Research Notices (2014) #2014 (14): 3912–3918.
[Summary]

The chromatic number of the defining graph of a RAAG provides an obstruction to embedding the RAAG into a mapping class group. More precisely, if A(Γ) embeds into the mapping class group of a surface S, then the chromatic number of Γ is bounded by a function of the complexity of S. This gives a simple graph-theoretic necessary condition for RAAG embeddings into mapping class groups.

[Journal] [Arxiv]
[cite]
```
@article {MR3239092,
    AUTHOR = {Kim, Sang-Hyun and Koberda, Thomas},
     TITLE = {An obstruction to embedding right-angled {A}rtin groups in
              mapping class groups},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2014},
    NUMBER = {14},
     PAGES = {3912--3918},
      ISSN = {1073-7928,1687-0247},
   MRCLASS = {20F65},
  MRNUMBER = {3239092},
MRREVIEWER = {Kevin\ D.\ Schreve},
       DOI = {10.1093/imrn/rnt064},
       URL = {https://doi.org/10.1093/imrn/rnt064},
}
```
8. Sang-hyun Kim and Thomas Koberda. Embeddability between right-angled Artin groups, Geometry & Topology 17 (2013) 493–530.
[Summary]

The notion of an "extension graph" associated to a RAAG is introduced and shown to provide a systematic tool for studying embeddings between RAAGs. Specifically, A(Γ) embeds into A(Λ) whenever Γ appears as an induced subgraph of the extension graph of A(Λ). This unifies and extends previous ad hoc constructions, yielding many new embedding results and establishing a conceptual framework for the embeddability problem.

[Journal] [Arxiv]
[cite]
```
@article {MR3039768,
    AUTHOR = {Kim, Sang-hyun and Koberda, Thomas},
     TITLE = {Embedability between right-angled {A}rtin groups},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {17},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {493--530},
      ISSN = {1465-3060,1364-0380},
   MRCLASS = {20F36 (05C25 20E05 20F05)},
  MRNUMBER = {3039768},
MRREVIEWER = {Yago\ Antol\'{\i}n},
       DOI = {10.2140/gt.2013.17.493},
       URL = {https://doi.org/10.2140/gt.2013.17.493},
}
```
7. Sang-hyun Kim and Henry Wilton. Polygonal words in free groups, Quarterly Journal of Mathematics (2012) 63(2), 399–421.
[Summary]

The notion of "polygonal" words in free groups is introduced, capturing words whose associated van Kampen diagrams over any double of the free group admit a CAT(−1) metric. These words are shown to be plentiful and are used to construct surface subgroups in doubles of free groups. This provides strong evidence for Gromov's question on the ubiquity of surface subgroups in word-hyperbolic groups.

[Journal] [Arxiv]
[cite]
```
@article {MR2925298,
    AUTHOR = {Kim, Sang-Hyun and Wilton, Henry},
     TITLE = {Polygonal words in free groups},
   JOURNAL = {Q. J. Math.},
  FJOURNAL = {The Quarterly Journal of Mathematics},
    VOLUME = {63},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {399--421},
      ISSN = {0033-5606,1464-3847},
   MRCLASS = {20F10 (03D40 20E05 20F67 68R15)},
  MRNUMBER = {2925298},
MRREVIEWER = {Serge\ Perrine},
       DOI = {10.1093/qmath/haq045},
       URL = {https://doi.org/10.1093/qmath/haq045},
}
```
6. Sang-hyun Kim. Surface subgroups of graph products of groups, International Journal of Algebra and Computation (2012) 22 (8).
[Summary]

For a graph product of groups, the kernel of the natural map to the direct product of vertex groups is shown to embed into a RAAG. When each vertex group is finite or cyclic, the graph product is virtually special in the sense of Haglund and Wise. As a consequence, for graphs on at most seven vertices, right-angled Coxeter groups contain hyperbolic surface subgroups if and only if the underlying graph is weakly chordal.

[Journal] [Arxiv]
[cite]
```
@article {MR3010817,
    AUTHOR = {Kim, Sang-Hyun},
     TITLE = {Surface subgroups of graph products of groups},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {22},
      YEAR = {2012},
    NUMBER = {8},
     PAGES = {1240003, 20},
      ISSN = {0218-1967,1793-6500},
   MRCLASS = {20F65 (20F36)},
  MRNUMBER = {3010817},
       DOI = {10.1142/S0218196712400036},
       URL = {https://doi.org/10.1142/S0218196712400036},
}
```

5. Sang-hyun Kim. Geometricity and polygonality in free groups, International Journal of Algebra and Computation 21(1–2) (2011) 235–256.

[Summary]

"Geometric" words in free groups, as defined by Gordon and Wilton, are shown to be "polygonal" in the sense of the companion work on polygonal words. This connects two independent approaches to Gromov's question on surface subgroups: geometric words arising from immersed surfaces and polygonal words arising from CAT(−1) van Kampen diagrams.

[Journal] [Arxiv]

[cite]

@article {MR2787460,
    AUTHOR = {Kim, Sang-Hyun},
     TITLE = {Geometricity and polygonality in free groups},
   JOURNAL = {Internat. J. Algebra Comput.},
  FJOURNAL = {International Journal of Algebra and Computation},
    VOLUME = {21},
      YEAR = {2011},
    NUMBER = {1-2},
     PAGES = {235--256},
      ISSN = {0218-1967,1793-6500},
   MRCLASS = {20F65 (20E06 20F67)},
  MRNUMBER = {2787460},
MRREVIEWER = {Jos\'{e}\ Burillo},
       DOI = {10.1142/S0218196711006157},
       URL = {https://doi.org/10.1142/S0218196711006157},
}

4. Sang-hyun Kim. On right-angled Artin groups without surface subgroups, Groups, Geometry, and Dynamics 4(2) (2010) 275–307.
[Summary]

A combination theorem is proved for the class of right-angled Artin groups that do not contain closed hyperbolic surface subgroups: certain amalgamations and HNN extensions preserve this property. The proof relies on the theory of special cube complexes. This provides a structural characterization of surface-subgroup-free RAAGs and contributes to the understanding of which RAAGs arise as fundamental groups of non-positively curved spaces.

[Journal] [Arxiv]
[cite]
```
@article {MR2595093,
    AUTHOR = {Kim, Sang-hyun},
     TITLE = {On right-angled {A}rtin groups without surface subgroups},
   JOURNAL = {Groups Geom. Dyn.},
  FJOURNAL = {Groups, Geometry, and Dynamics},
    VOLUME = {4},
      YEAR = {2010},
    NUMBER = {2},
     PAGES = {275--307},
      ISSN = {1661-7207,1661-7215},
   MRCLASS = {20F36 (05C25 20F65 57M07)},
  MRNUMBER = {2595093},
MRREVIEWER = {Matthew\ B.\ Day},
       DOI = {10.4171/GGD/84},
       URL = {https://doi.org/10.4171/GGD/84},
}
```
3. Chan-Byoung Chae, Sang-hyun Kim and Robert W. Heath Jr., Linear network coordinated beamforming for cell-boundary users, Proc. of IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC) (2009).
[Summary]

A linear coordinated beamforming strategy is proposed for multi-cell wireless networks to mitigate inter-cell interference affecting cell-boundary users. Adjacent base stations cooperatively optimize their transmitted beams to steer nulls toward vulnerable cell-edge users in neighboring cells. Simulations confirm that this coordination significantly improves signal quality and overall downlink throughput compared to uncoordinated methods.

[Journal]
[cite]
```
@inproceedings{spawc2009chae,
  author={Chae, Chan-Byoung and Kim, Sang-hyun and Heath, Robert W.},
  booktitle={2009 IEEE 10th Workshop on Signal Processing Advances in Wireless Communications (SPAWC)}, 
  title={Linear network coordinated beamforming for cell-boundary users}, 
  year={2009},
  pages={534-538},
  doi={10.1109/SPAWC.2009.5161842}
}
```
2. Chan-Byoung Chae, Sang-hyun Kim and Robert W. Heath Jr., Network coordinated beamforming for cell-boundary users: linear and non-linear approaches, IEEE Journal of Selected Topics in Signal Processing (J-STSP), vol. 3, no. 6 (2009) 1094–1105.
[Summary]

Both linear and non-linear network coordinated beamforming algorithms are developed for multi-cell downlink environments with multi-antenna users at cell boundaries. The algorithms transmit independent data streams while suppressing mutual interference through cooperative coordination among base stations. The non-linear approach further optimizes spatial resources by decoupling the interacting channels, yielding substantial throughput and reliability gains over uncoordinated methods.

[Journal]
[cite]
```
@article{jstsp2009chae,
  author={Chae, Chan-Byoung and Kim, Sang-hyun and Heath, Robert W.},
  journal={IEEE Journal of Selected Topics in Signal Processing}, 
  title={Network coordinated beamforming for cell-boundary users: linear and non-linear approaches}, 
  year={2009},
  volume={3},
  number={6},
  pages={1094-1105},
  doi={10.1109/JSTSP.2009.2035857}
}
```
1. Sang-hyun Kim. Co-contractions of graphs and right-angled Artin groups, Algebraic and Geometric Topology 8 (2008) 849–868.
[Summary]

A natural map between right-angled Artin groups induced by a "co-contraction" of the underlying defining graphs is shown to be injective. The family of "contraction words" in free groups that yield such graph co-contractions is explicitly characterized. This provides a systematic method for constructing embeddings between RAAGs from combinatorial operations on graphs.

[Journal] [Arxiv]
[cite]
```
@article {MR2443098,
    AUTHOR = {Kim, Sang-hyun},
     TITLE = {Co-contractions of graphs and right-angled {A}rtin groups},
   JOURNAL = {Algebr. Geom. Topol.},
  FJOURNAL = {Algebraic \& Geometric Topology},
    VOLUME = {8},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {849--868},
      ISSN = {1472-2747,1472-2739},
   MRCLASS = {20F65 (20F36)},
  MRNUMBER = {2443098},
       DOI = {10.2140/agt.2008.8.849},
       URL = {https://doi.org/10.2140/agt.2008.8.849},
}
```

Submitted or Accepted Papers

7. TBA on Samurai (2026).

[Summary]

Details of this paper will be posted as soon as the preprint becomes available.

6. Aletheia tackles FirstProof autonomously (2026).

[Summary]

This report describes the performance of Aletheia, an autonomous mathematics research agent powered by Gemini, on the FirstProof challenge—a set of 10 research-level open problems in mathematics. Aletheia solved 6 of the 10 problems autonomously within the challenge timeframe, with solutions verified by expert mathematicians. The agent architecture, prompts, and detailed inference traces are open-sourced to enable community verification and further development.

[Arxiv]

[cite]

@misc{arxiv:2602.21201,
      title={Aletheia tackles FirstProof autonomously}, 
      author={Tony Feng and Junehyuk Jung and Sang-hyun Kim and Carlo Pagano and Sergei Gukov and Chiang-Chiang Tsai and David Woodruff and Adel Javanmard and Aryan Mokhtari and Dawsen Hwang and Yuri Chervonyi and Jonathan N. Lee and Garrett Bingham and Trieu H. Trinh and Vahab Mirrokni and Quoc V. Le and Thang Luong},
      year={2026},
      eprint={2602.21201},
      archivePrefix={arXiv},
      primaryClass={math.GR},
      url={https://arxiv.org/abs/2602.21201}
}

5. Towards Autonomous Mathematics Research (2026).

[Summary]

This paper introduces Aletheia, a research agent designed for autonomous mathematical exploration and proof generation. Aletheia integrates large language model capabilities with symbolic verification and literature search to conduct multi-step mathematical reasoning over extended horizons. The system is evaluated on open problems in combinatorics, number theory, and algebra, demonstrating progress toward AI-assisted autonomous mathematical discovery.

[Arxiv]

[cite]

@misc{arxiv:2602.10177,
      title={Towards Autonomous Mathematics Research}, 
      author={Tony Feng and Trieu H. Trinh and Garrett Bingham and Dawsen Hwang and Yuri Chervonyi and Junehyuk Jung and Joonkyung Lee and Carlo Pagano and Sang-hyun Kim and Federico Pasqualotto and Sergei Gukov and Jonathan N. Lee and Junsu Kim and Kaiying Hou and Golnaz Ghiasi and Yi Tay and YaGuang Li and Chenkai Kuang and Yuan Liu and Hanzhao Lin and Evan Zheran Liu and Nigamaa Nayakanti and Xiaomeng Yang and Heng-Tze Cheng and Demis Hassabis and Koray Kavukcuoglu and Quoc V. Le and Thang Luong},
      year={2026},
      eprint={2602.10177},
      archivePrefix={arXiv},
      primaryClass={math.GR},
      url={https://arxiv.org/abs/2602.10177}
}

4. Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems (2026).

[Summary]

A Gemini-based AI agent is used to systematically evaluate 700 open conjectures from Bloom's Erdős Problems database. Using AI-driven verification to narrow the search space followed by human expert evaluation, 13 problems are addressed: 5 through novel autonomous solutions and 8 through identification of existing solutions in the literature. The study demonstrates a viable methodology for semi-autonomous mathematical discovery at scale.

[Arxiv]

[cite]

@misc{arxiv:2601.22401,
      title={Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems}, 
      author={Tony Feng and Trieu Trinh and Garrett Bingham and Jiwon Kang and Shengtong Zhang and Sang-hyun Kim and Kevin Barreto and Carl Schildkraut and Junehyuk Jung and Jaehyeon Seo and Carlo Pagano and Yuri Chervonyi and Dawsen Hwang and Kaiying Hou and Sergei Gukov and Cheng-Chiang Tsai and Hyunwoo Choi and Youngbeom Jin and Wei-Yuan Li and Hao-An Wu and Ruey-An Shiu and Yu-Sheng Shih and Quoc V. Le and Thang Luong},
      year={2026},
      eprint={2601.22401},
      archivePrefix={arXiv},
      primaryClass={math.GR},
      url={https://arxiv.org/abs/2601.22401}
}

3. Irrationality of rapidly converging series: a problem of Erdős and Graham (2026).
[Summary]

An open problem of Erdős and Graham on the irrationality of rapidly converging series is resolved. It is shown that if a sequence of positive integers grows at least as fast as the golden ratio raised to a double exponential, then the sum ∑ 1/(a_n a_{n+1}) is irrational. The result is further generalized to sums of the form ∑ 1/(a_n a_{n+k}), extending the scope of classical irrationality criteria for series defined by fast-growing integer sequences.

[Arxiv]
[cite]
```
@misc{arxiv:2601.21442,
      title={Irrationality of rapidly converging series: a problem of Erdős and Graham}, 
      author={Kevin Barreto and Jiwon Kang and Sang-hyun Kim and Vjekoslav Kovač and Shengtong Zhang},
      year={2026},
      eprint={2601.21442},
      archivePrefix={arXiv},
      primaryClass={math.GR},
      url={https://arxiv.org/abs/2601.21442}
}
```
2. Elementary equivalence and diffeomorphism groups of smooth manifolds (2025).
[Summary]

If the diffeomorphism groups Diff^r(M) and Diff^s(N) of two smooth manifolds are elementarily equivalent as groups in first-order logic, then M and N are diffeomorphic and r = s. This extends classical reconstruction theorems of Takens and Filipkiewicz from group isomorphisms to elementary equivalence, a strictly weaker condition. The result demonstrates that first-order logic alone is sufficient to recover both the smooth topology of a manifold and the regularity of its diffeomorphism group.

[Arxiv]
[cite]
```
@misc{arxiv:2507.07427,
      title={Elementary equivalence and diffeomorphism groups of smooth manifolds}, 
      author={Sang-hyun Kim and Thomas Koberda and J. de la Nuez González},
      year={2026},
      eprint={2507.07427},
      archivePrefix={arXiv},
      primaryClass={math.GR},
      url={https://arxiv.org/abs/2507.07427}
}
```
1. Jaewon Chang, Sang-hyun Kim and Thomas Koberda. Algebraic Structure of Diffeomorphism Groups of One-Manifolds, accepted, Panoramas et synthèses - Société mathématique de France.
[Summary]

This expository article gives a detailed account of Mather's theorem on the simplicity of diffeomorphism groups, specialized to one-manifolds. By restricting to dimension one, the exposition avoids higher-dimensional technicalities and isolates the core geometric and dynamical mechanisms underlying Mather's proof. The smoothing techniques and fragmentation lemmas that form the backbone of the argument are carefully developed, providing an accessible entry point for researchers studying the algebraic structure of transformation groups.

[Journal] [Arxiv]
[cite]
```
@misc{arxiv:1904.08793,
      title={Algebraic Structure of Diffeomorphism Groups of One-Manifolds}, 
      author={Jaewon Chang and Sang-hyun Kim and Thomas Koberda},
      year={2026},
      eprint={1904.08793},
      archivePrefix={arXiv},
      primaryClass={math.GR},
      url={https://arxiv.org/abs/1904.08793}
}
```

Unpublished notes

2. The Arens space $S_2$ is a paracomplex: A note on Nagata's Problem 3.

[Summary]

In 1974, J. Nagata posed the problem of finding a paracomplex that is not the closed continuous image of any metric space. We prove that Arens space $S_2$ is such an example.

[Journal]

1. Sang-hyun Kim, Thomas Koberda and Juyoung Lee. Finite subgraphs of extension graphs.

[Summary]

A strengthening and also a very detailed proof of Lemma 3.1 that originally appeared in Embedability between right-angled Artin groups , Geometry & Topology 17 (2013) 493--530.

[Arxiv]

[cite]

@misc{arxiv:1708.02088,
      title={Finite subgraphs of an extension graph}, 
      author={Sang-hyun Kim and Thomas Koberda and Juyoung Lee},
      year={2026},
      eprint={1708.02088},
      archivePrefix={arXiv},
      primaryClass={math.GR},
      url={https://arxiv.org/abs/1708.02088}
}

Slides and videos

A problem set for my two-hour introductory lecture to hyperbolic geometry
H. Short's proof of Howson's property for free groups (2012 KAIST graduate class)
Free products of finite groups are virtually free (2012 KAIST graduate class)
Nielsen generating set of Aut(Fn) (2012 KAIST graduate class)
Finitely generated residually finite groups are Hopfian (2012 KAIST graduate class)

Talks & Panel

Upcoming

1. Siji High School, Daegu, Korea. November 24, 2026.
2. Ulsan Mathematical Culture Center, October 24, 2026
3. New Developments of Teichmüller Theory (Oberwolfach Workshop), September 28 - Oct 2, 2026
4. Korean Association for Logic Meeting, August 18, 2026
5. KAOS Talk Concert, August 1, 2026, Yonsei 100th Memorial Building, Seoul, Korea
6. 2K-GATE Workshop, Jeju Island, Korea, July 27, 2026
7. Busan Mathematics Culture Center, July 10, 2026 (2 - 4 pm)
8. HCMC Spring Public Lecture Series, June 13, 2026, KIAS, Seoul, Korea [Link]
9. Current Challenges in Topology, Milan, Italy, May 20 - 24, 2026
10. Kangwon Cultural Education Center, May 6, 2026 (2 - 4 pm)
11. CRUNCH seminar, April 24, 2026 (1 - 1:45 am KST) [YouTube]

Complete Talks

▶ Click to expand all 280 completed talks

IMU-KIAS Colloquia, hosted with the IMU Executive Committee, KIAS, March 11 - 13, 2026.
Daegu Gosan Library, April 10, 2026 (7 - 9 pm)
Career Lecture at the Graduation Ceremony, the Gifted Education Center, the Chungcheongbuk-do Institute of Science Education, October 18, 2025.
The 6th Workshop on Geometry and Topology around Young-Nam, September 26 - 27, 2025.
Hyundai Motor Group, August 13, 19, 26, 2025.
Topology seminar, National University of Singapore, July 30, 2025.
Non-positive curvature and applications, Isaac Newton Institute, July 7 - 11, 2025.
Daejeon Institute of Education Information, June 26, 2025. (public math, "human, mathematics and computer")
Geometric Group Theory and Related Topics, June 16 - 20, 2025, BICMR. [Link]
Mathematics Colloquium, April 16 (Wed), 2025, Kyungpook National University
East Asian Conference on Geometric Topology 20, Tokyo, Japan, February 4, 2025.
Friday Seminar on Knot Theory, OCAMI, Osaka, Japan, January 31, 2025.
What is...? (on rotation number), Osaka University, Japan, January 30, 2025.
2025 KMS-VMS Joint Workshop, Hanoi, Vietnam, January 6 - 10, 2025.
Geometry and Dynamics in Low-Dimensions, Hanoi, Vietnam, Janury 6 - 10, 2025.
On Dream Young Mathematicians Camp (for high school students), January 5, 2025.
Topology Seminar, National University of Singapore, December 26, 2024.
Foliations and Diffeomorphism Groups, CIRM, Marseille, December 9 - 13, 2024.
Dynamical Group Theory V (KOREA: KIAS workshop on One RElator groups and other Aspects of GGT), September 27, 2024. [Link]
KAIST, Basic Science Week, October 30, 2024.
Davinci Motel by Hyundai Card, Seoul, September 28, 2024. (public math, invitation- only meeting)
Dynamical Group Theory IV (KIAS-Rice Workshop), September 27, 2024. [Link]
Public Lecture, Huh June Center for Mathematical Challenges, September 7, 2024. [Link]
Colloquium, Huh June Center for Mathematical Challenges, September 5, 2024.
Public Lecture organized by Korea Academy of Science and Technology (KAST), Seoul Science High School, August 19, 2024.
Panel Discussion, World Congress of Korean and Korean-Ethnic Scientists and Engineers, Seoul, July 11, 2024.
KFAS Summer 2024, Gangneung, Korea, July 4 - 6, 2024.
KAOS Science, "100 years of geometric topology and the Poincaré conjecture", July 3, 2024 [Stream Link] (recording: June 17)
REU Colloquium, University of Virginia, June 19, 2024 (8 PM, US EST) / June 20, 2024 (9 AM, KST) : online.
Computational aspects of thin groups, Institute for Mathematical Sciences National University of Singapore, June 11, 2024.
An-ahm Lecture, Korea University, May 20, 2024
Low Dimensional Actions, IHP (Institute Henri Poincaré), Paris, April 29 - May 3,
[Link]
Oberseminar Differentialgeometrie, Max Planck Institute for Mathematics, April 25,
[Link]
Special Session on Geometric Structures and Representation Spaces, Korean Mathematical Society , KAIST, Daejeon, April 20, 2024.
Colloquium, KRIMS, Kangwon University, April 17, 2024.
Math Colloquium, Postech, Pohang, March 22, 2024. [Link]
The 19th East Asian Conference of Geometric Topology, Kyoto, Japan, February 19 - 23, 2024.
KAIST Geometric Topology Fair 2024, Busan, Jan 15 - 19, 2024
Round table discussion on publicizing science culture, Ministry of Science and ICT, Korea, January 10, 2024, [news]
"What is a good mathematical research?", The Third Round Table -- Mathematics for Tomorrow, old and new", The Korean Federation of Science and Technology Societies (KOFST), Korea, December 20, 2023 [YouTube]
Department Colloquium, Yonsei University, Seoul, Korea, November 9, 2023 (5 pm).
Dream Lecture Series by Korea Foundation for Advanced Studies, West Daejeon Highschool, Oct 18, 2023.
The 4th Korea-France Conference in Mathematics, August 21 - 25, 2023, KIAS, Korea.
Teichmüller Theory: Classical, Higher, Super and Quantum, Mathematisches Forschungsinstitut Oberwolfach, Germany, July 30 - Aug 4, 2023. Title: Optimal independent system for Gamma0(p) and Gamma0(pq).
Characters and Moduli of Surfaces (SerFest), The Research Institute for Mathematical Sciences (RIMS), Kyoto, Japan, July 19 - 21, 2023.
The Mathematical Society of Japan -- Seasonal Institute (MSJ-SI), New aspects of Teichmüller theory, University of Tokyo, Japan, July 9 - 15, 2023.
Korea Foundation for the Advancement Science & Creativity, International Olympiad Team Ceremony, June 14, 2023.
NCTS 2023 dynamics workshop (minicourse of 3 talks), National Center for Theoretical Sciences (NCTS), National Taiwan University, Taiwan, June 8-10, 2023.
Topology Seminar, Gakushuin University, May 26, 2023.
Special Session on Geometric Structures and Representation Spaces, Korean Mathematical Society , April 28, 2023.
Topology seminar, Seoul National University, April 21, 2023.
The 3rd Probabilistic Methods in Negative Curvature workshop (minicourse of 4 talks), ICTS Bangalore, India, February 27 -- March 10, 2023 (mini-course).
Conformal dynamics and groups, BICMR, December 2, 2022 (online).
The Pacific Rim Mathematical Association Congress 2022 (PRIMA CONGRESS 2022), Vancouver, Canada, Special Session on ``Geometric Group Theory'', December 2022 (TBD).
School on Dynamical Group Theory, Dijon, France, Oct 3 - 7, 2022 (mini-course of 3 talks).
Mathematics Department Colloquium, Sookmyung Women's University, September 15, 2022.
REU Colloquium, University of Virginia, July 27, 2022 (US EST) / July 28, 2022 (KST) : online.
Topology and Geometry Seminar, National University of Singapore, July 4, 2022.
Regular Workshop, Integrative Research Institute in Basic Science, Soongsil University, June 24, 2022.
Geometry and Analysis on Groups Research Seminar, University of Vienna, June 7,
OpenKIAS Public Lecture, Korean Mathematical Society, April 28, 2022 (5pm), hybrid.
"공간의 풍경 (The landscape of a space), KIAS Public Lecture, Korean Mathematical Society Spring Meeting, April 28, 2022. [Youtube]
Sydney Mathematical Research Institute (SMRI) Algebra and Geometry Online seminar, March 2nd, 2022 (Wed, 11 am KST/ 1 pm Australia). [youtube]
Future intelligence (forum), CHUNG MONG-KOO Foundation and Chosun Ilbo, February 17, 2022. [youtube] [youtube (sketch)] [news article]
Samsung Sciences & Technology Foundation Annual Forum, November 22, 2021.
Geometry and Topology Online, Warwick Mathematics Institute, November 18, 2021 (online).
Human, Mathematics, Computer (On the Halting problem of Turing), KFAS building, Dream Lecture Series by Korea Foundation for Advanced Studies, November 13,
Symmetry in Newcastle (seminar), The University of Newcastle, Australia, November 1, 2021 (online). [youtube]
Graduate seminar on mathematical challenges, Yonsei University, October 6, 2021.
VI Congreso Latinoamericano de Matemáticos (CLAM) 2021, Montevideo, Uruguay, September 14, 2021 (online).
REU Colloquium, University of Virginia, July 21, 2021 (online).
Mathematical Sciences Department colloquium, Seoul National University, May 6,
"On Circle Diffeomorphism Groups" (online).
The 16th East Asian Conference on Geometric Topology, University of Tokyo, Japan, January 25, 2021. (online, invited talk)
OpenKIAS public lecture - 불가능에 대하여 (갈루아, 괴델, 튜링, 힐버트), December 22, 2020. [Youtube]
Expanding Dynamics, CMM - Center for Mathematical Modeling / Universidad de Chile, October 13, 2020. (online)
Teichmüller Theory: Classical, Higher, Super and Quantum, CIRM, Luminy, France, October 8, 2020. (online)
The 3rd International Undergraduate Mathematics Summer School, Seoul National University,TBD, 5 lectures, postponed.
Mathematics Colloquium, Seoul National University, Korea, TBD. Groups of circle diffeomorphisms: analysis, dynamics and algebra, postponed.
이토록 황홀한 수학 (Fascinated by Mathematics), a series of 11 lectures on various subjects, EBS2 channel (Korean Educational Broadcasting System), August 19 - September 2, 2020. lecture 1 (youtube) complete lectures
REU Colloquium, University of Virginia, June 24, 2020 (online).
Colloquium at Electrical Engineering School, DGIST, Korea, June 2, 2020 (online).
Hyperbolic Lunch, University of Toronto, May 13, 2020. (online)
Virtual Seminar on Geometry and Topology (visgat), KIAS and KAIST, March 31,
(online)
Topology Seminar, Gakushuin University, December 2, 2019.
Mathematics Colloquium, KAIST, November 21, 2019.
Mathematics Colloquium, Korea University, November 15, 2019.
Arbeitsgemeinschaft: Zimmer's Conjecture, Mathematisches Forschungsinstitut Oberwolfach, Germany, 13 -- 18 October, 2019. Title: Property T and actions on S^1.
Geometry and Analysis on Groups Seminar, University of Vienna, Austria, October 8,
Summer School on Geometric Topology and Algebraic Geometry, KAIST, Korea, August 12 an 13, 2019.
Combinatorial and algebraic aspects of geometric structures – Workshop in Thailand, with the cooperation of Luxembourg, Singapore, and Thailand, Chiang Mai, Thailand, July 18 and 19, 2019.
Ordered Groups and Rigidity in Dynamics and Topology, Oaxaca, Mexico, June 17,
Undergraduate seminar, Kwangwoon University, June 7, 2019.
International Conference Complex Analysis, Partial Differential Equations And Their Applications, Hanoi, Vietnam, June 5, 2019. *My talk was on June 5, but it did not appear in the webpage for some reason.
Ergodic and Geometric Group (EGG) Theory seminar, EPFL, Lausanne, Swiss, May 27, 2019.
Non-positive curvature, Warsaw, Poland, May 20, 2019.
Geometry and Analysis on Groups Seminar, University of Vienna, Austria, May 16,
Public lecture at Mathematics Culture Festival, Gwachun National Science Museum, Korea, April 27, 2019.
Public lecture (organized by The Korean Academy of Science and Technology), Yeongnam High School, Daegu, Korea, April 3, 2019.
Special Sessions on Mapping Class Groups, University of Hawaii at Manoa, Honolulu, US, March 23, 2019.
The 14th East Asian Conference of Geometric Topology, Beijing, China, January 23,
(plenary)
Suzhou 2019 Workshop on Geometry Topology, Soochow University, Suzhou, China, January 18, 2019.
Boundaries of topological groups, C*-algebras, symmetric spaces, and Lyapounov exponents, TSIMF, Sanya, China, December 20, 2018.
One-day Workshop about Dynamics, Geometry and Groups, Suwon, Korea, December 5, 2018.
KIAS Analysis Seminar, Seoul, Korea, November 1, 2018.
New Trends in Teichmüller Theory and Mapping Class Groups, Mathematisches Forschungsinstitut Oberwolfach, Germany, September 2--8, 2018.
Department Seminar, Chiang Mai University, Thailand, August 24, 2018.
Talk concert (for general public), Gwachun National Science Museum, Korea, Aug 19,
Science Camp, College of Natural Sciences, Seoul National University, (1) August 3, 2016 (2) August 9, 2018.
International Conference on Dynamical Systems, Sustech, China, June 25--28, 2018. Slide (PDF)
Hyperbolic 3-manifolds and related topics, Postech, Korea, June 18-- 22, 2018.
Silk Road Geometry Conference, Gokova Geometry/Topology Institute (GGTI), Turkey, June 4 - 8, 2018.
Dream Lecture Series by Korea Foundation for Advanced Studies, Hanyoung Foreign Language High School, May 14, 2018.
Dream Lecture Series by Korea Foundation for Advanced Studies, KFAS building, May 12, 2018.
Topology in Australia and South Korea, IBS-CGP, Korea, April 25--27, 2018.
KIAS (Korea Institute for Advanced Study), Korea, April 17, 2018.
Topology Seminar, KAIST, Korea, March 27, 2018.
Branched Coverings, Degenerations, and Related Topics 2018 (minicourse), Hiroshima University, Japan, March 5 - 9, 2018.
Structure of 3-manifold Groups, CIRM (Luminy), France, February 26 - March 2,
Workshop on Geometric Group Theory (minicourse), BICMR, Beijing University, December 16 - 17, 2017.
Kyoto University, December 12, 2017.
Low-dimensional topology seminar, Osaka University, December 5, 2017.
Topology Seminar, University of Tokyo, November 28, 2017.
Max Dehn Seminar, University of Utah, October 25, 2017.
Topology Seminar, Rice University, October 23, 2017.
Topology Seminar, University of Texas at Austin, October 20, 2017.
Colloquium, University of Virginia, October 12, 2017.
Geometric Group Theory and Topology Seminar, Tufts University, October 3, 2017.
Geometry and Topology Seminar, Brown University, September 29, 2017.
GGT Seminar, MgGill University, September 27, 2017.
Japan Conference on Discrete and Computational Geometry, Graphs, and Games: JCDCG3, Tokyo University of Science (Aug 29 - Sep 1), Tokyo, Japan, August 29,
Japanese Topology Symposium, Tokai University, Tokyo, Japan, August 21 -- 24, 2017, 2017.
Invited talk, Korea Institute for Advanced Study (KIAS), Korea, Aug 7, 2017.
Dream Lecture Series by Korea Foundation for Advanced Studies, KFAS building, July 15, 2017.
GAGTA 2017: Geometric and Asymptotic Group Theory with Applications (July 3 -- 7), Bilbao, Spain, July 4, 2017.
SFB Seminar, Universität Regensburg, Germany, June 30, 2017.
Séminaire Géométrie, Dynamique et Topologie (GDT), L’Institut de Mathématiques de Marseille (I2M), France, May 22, 2017.
Geometry Seminar, ETH Zürich, Swiss, May 3, 2017.
Ergodic and Geometric Group (EGG) Theory seminar, EPFL, Lausanne, Swiss, April 27, 2017.
Thursday Colloquium, TIFR, Mumbai, India, April 20, 2017.
IBS--CGP Seminar, Pohang, Korea, April 13, 2017.
Department Colloquium, Sungkyunkwan University, Suwon, Korea, April 6, 2017.
Dream Lecture Series by Korea Foundation for Advanced Studies, Young-rak High School, March 20, 2017.
Topology--Geometry Seminar, Hiroshima University, Japan, March 16, 2017.
Topology Seminar, Osaka University, Japan, March 13, 2017.
Young Mathematicians' Camp, National Institute for Mathematical Sciences, Daejeon, February 22, 2017.
SNU Geometry and Topology Mini-Workshop, Seoul National University, Korea, February 17, 2017.
College of Natural Sciences Public Lecture, Seoul National University, Korea, February 9, 2017. [youtube]
SNU Topology Winter School, December 16,, 2016.
Virginia Topology Conference, University of Virginia, November 18, 2016.
Geometry and Topology Seminar, Seoul National University, November 16, 2016.
Topology Seminar, Sungkyunkwan University, November 15, 2016.
Invited Talk, Korean Mathematical Society Annual Fall Conference, October 22, 2016.
Dream Lecture Series by Korea Foundation for Advanced Studies, Seoul High School, October 14, 2016.
Workshop on Moduli Spaces of Geometric Structures, a part of the summer-long program Geometry, Topology and Dynamics of Moduli Spaces, National University of Singapore, August 17, 2016.
Dream Lecture Series by Korea Foundation for Advanced Studies, KFAS building, July 23, and July 30, 2016.
Geometric Topology Fair 2016, KAIST, Daejeon, July 7, 2016.
GAGTA (Geometric and Asymptotic Group Theory and Applications) 2016, Stevens Institute of Technology, June 17, 2016.
IBS--CGP seminar, IBS--CGP, Pohang, Korea, April 21, 2016.
Saturday Public Science Lectures, College of Natural Sciences, Seoul National University, March 26, 2016.
Mathematics seminar, Konkuk University, Seoul, Korea, March 25, 2016.
Invited lecture, Korea Institute for Advanced Study (KIAS), Korea, Mar 2, 2016.
Group actions seminar, Yale University, Feb 22, 2016.
Geometry and topology seminar, Univ. of Massachusetts at Amherst, Feb 19, 2016.
Geometric group theory seminar, Tufts University, Feb 18, 2016.
Teichmüller theory and low-dimensional topology, Tsinghua Sanya International Mathematics Forum (TSIMF), China, Jan 11 - 15, 2016.
East Asian Conference on Algebraic Topology 6 (EACAT-6), Daejeon, November 30 - Dec 4, 2015.
2015 International Workshop on Mathematical Sciences in Dalian, China, Oct 30 - Nov 1, 2015.
Saturday Public Science Lecture, College of Natural Sciences, Seoul National University, Oct 24, 2015.
Department Colloquium, Ewha Women's University, Oct 15, 2015.
University of Rennes, France, October 1, 2015.
Dream Lecture Series by Korea Foundation for Advanced Studies, Chil-won High School - October 16, 2015.
Dream Lecture Series by Korea Foundation for Advanced Studies, Seo-oon Middle School - September 4, 2015.
IBS--CGP Mathematics Festival for Undergraduates, Aug 17 - 21, 2015.
Dubrovnik VIII - Geometric Topology, Geometric Group Theory and Dynamical Systems, Croatia, June 22 - 26, 2015.
Statistics seminar, Seoul National University, Korea, June 4, 2015.
Dream Lecture Series by Korea Foundation for Advanced Studies, Seocho High School - May 29, 2015.
Dream Lecture Series by Korea Foundation for Advanced Studies, Kyungshin High School - May 8, 2015.
Geometry & Topology seminar, Postech, Korea, April 22, 2015.
Geometric Group Theory on Gulf Coast (G^3), San Padres Island, USA, March 26 - 29, 2015.
KIAS Algebra Seminar, KIAS, January 5, 2015.
Dream Lecture Series by Korea Foundation for Advanced Studies, KFAS building, December 20, 2014.
Group Action Forum, Tsinghua Sanya International Mathematics Forum, China, December 15 -- 19, 2014.
KIAS/CMC Colloquium, KIAS, December 2, 2014.
Department Colloquium, Chiang Mai University, October 28, 2014.
Dream Lecture Series by Korea Foundation for Advanced Studies, Banpo High School, September 13, 2014.
the 7th Mathematical Society of Japan -- Seasonal Institute (MSJ-SI), Hyperbolic Geometry and Geometric Group Theory (ICM Satellite), University of Tokyo, Japan, July 30 - August 5, 2014.
Discrete Groups and Geometric Structures with Applications V , KU Leuven, Belgium, June 2 - 6, 2014.
Seoul National University Department Colloquium, Subgroups of Mapping Class Groups, March 13, 2014
Branched Coverings, Degenerations, and Related Topics 2014, Hiroshima University, Japan, March 7, 2014.
Groups and Geometry in the South East, Mathematics Institute, Warwick University, United Kingdom, February 21, 2014.
Complex Analysis and Topology of Discrete Groups and Hyperbolic Spaces, Research Institute for Mathematical Sciences, Kyoto University, Japan, January 24, 2014.
5th East Asian Conference of Algebraic Topology (EACAT 5), Chinese Academy of Sciences, Beijing, China, December 3, 2013.
Wasatch Topology Conference, the University of Utah, USA, November 16, 2013.
Topology Seminar, University of Texas at Austin, November 11, 2013.
Geometry and Topology Seminar, City University of New York, November 5, 2013.
Discovery-oriented class in calculus, Inha University Pedagogy Workshop, October 28, 2013.
Korean Mathematical Society Annual Meeting, University of Seoul, Korea, October 25, 2013.
Geometry and Topology Seminar, Brown University, October 9, 2013.
Topology/Geometry Seminar, Yale University, October 8, 2013.
New York Applied Algebra Colloquium, City University of New York, 27 September,
Geometric and Analytic Group Theory, Ventotene Island, Italy, September 9-14, 2013.
Geometric Structures on Low-Dimensional Manifolds, Korea Institute for Advanced Study, Korea, May 24, 2013.
Discrete Math Seminar, KAIST, April 19, 2013.
Hot Topics: Surface subgroups and cube complexes, Mathematical Sciences Research Institute, USA, March 19, 2013.
Topology and Geometry Seminar, National University of Singapore, February 13,
Geometric Group Theory and Topology Seminar, Tufts University, January 29, 2013.
Topology/Geometry Seminar, Yale University, January 22, 2013.
Manhattan Algebra Day, Stevens Institute, USA, December 7, 2012.
Topology Seminar, Osaka University, December 4 2012.
Friday Workshop on Geometry of Artin Groups, KIAS, November 23, 2012.
Topology Seminar, Hanyang University, October 19 and October 26, 2012.
Department Colloquium, Sogang University, October 18 2012.
MSJ-KMS Joint Meeting, Kyushu University, Japan, September 17, 2012.
Topology Seminar, KAIST, September 5 2012.
The 10th KAIST Geometric Topology Fair, KAIST, Daejeon, Korea, August 16, 2012.
Geometric and Asymptotic Group Theory with Applications (GAGTA-6), University of Duesseldorf, July 30, 2012.
Geometric Group Theory - Kyoto 2012, Kyoto University, Japan, June 7, 2012.
Department Colloquium, Ulsan University, April 12 2012.
Workshop on Immersed surfaces in 3-manifolds, a part of the IHP program "Geometry and analysis of surface group representations", IHP, Paris, March 26, 2012.
Geometry and Topology Seminar, SUNY Buffalo, January 25, 2012.
AMS-MAA Joint Meeting, Special session on hyperbolicity in manifolds and groups, Boston, January 4, 2012.
Department Colloquium, Konkuk University, Seoul, Korea, November 17, 2011.
Department Colloquium, Hanyang University, Seoul, Korea, November 4, 2011.
Department Colloquium, Yonsei University, Seoul, Korea, October 13, 2011.
Department Colloquium, Seoul National University, Seoul, Korea, September 29,
The 4th Topology Workshop, Chonbuk National University, Jeonju, Korea, August 23 - 24, 2011.
The 9th KAIST Geometric Topology Fair, KAIST, Daejeon, Korea, August 9, 2011.
Geometric and Asymptotic Group Theory with Applications (GAGTA--5), Universitat Politecnica de Catalunya, Barcelona, Spain, July 12, 2011.
Dubrovnik VII - Geometric Topology, Inter-University Centre and University of Zagreb, Dubrovnik, Croatia, July 2, 2011.
Geometry/Topology Seminar, University of Chicago, April 12, 2011.
Topology/Geometry Seminar, Yale University, April 5, 2011.
Spring Topology and Dynamics Conference, University of Texas at Tyler, U.S.A., March 18, 2011.
AMS Southeastern Section Meeting, Special Session on Geometric Group Theory, Georgia Southern University, U.S.A., March 13, 2011.
Topology and Geometric Group Theory Seminar, Cornell University, March 8, 2011.
Bernstein Seminar, Cornell University, March 8, 2011.
AMS-MAA Joint Meeting, Special session on groups, geometry and applications, New Orleans, January 7, 2011.
Topology Seminar, KAIST, Korea, December 23, 2010.
Geometry and Topology Seminar, SUNY Buffalo, November 19, 2010.
Topology Seminar, University of Texas at Austin, November 8, 2010.
Geometry and Topology Seminar, Caltech, October 22, 2010.
Approaches to Group Theory, Using Algebraic, Analytic, and Geometric Tools in the Study of Groups, Cornell University, U.S.A., October 10, 2010.
Topology Seminar, Brandeis University, September 21 2010.
Geometric Group Theory and Topology Seminar, Tufts University, September 14,
KAIST Topology Workshop, Daejeon, Korea, August 4, 2010.
KAIST--POSTECH--SNU YB Workshop, Jeonju, Korea, July 3, 2010.
Topology Seminar, University of California at Santa Barbara, May 18, 2010.
AMS Special Session on Geometric Group Theory, University of New Mexico, U.S.A., April 18 2010.
Geometric Group Theory Seminar, Tufts University, January 19, 2010.
BK21 Seminar, KAIST, January 26 2010.
Joint Topology and Discrete Math Seminar, KAIST, December 28, 2009.
Topology Seminar, Konkuk University, December 22, 2009.
Joint Meeting of Korean Mathematical Society and American Mathematical Society, Special Session on Geometric Structures and Geometric Group Theory, Ewha Womans University, Korea, December 18, 2009.
Topology/Geometry Seminar, Yale University, October 27, 2009.
Topology Seminar, The University of Texas at Austin, August 31, 2009.
International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory, the University of Nebraska-Lincoln, U.S.A., May 20, 2009.
AMS Special Session on Recent Progress in Geometric Group Theory, San Francisco State University, April 25, 2009.
Topology Seminar, The University of Texas at Austin, April 13, 2009.
Groups and Dynamics Seminar, Texas A&M University, March 25, 2009.
Topology Seminar, The University of Texas at Austin, October 27, 2008.
Groups and Infinite Graphs, Erwin Schroedinger International Institute, Austria, August 26, 2008.
Topology Seminar, Seoul National University, Korea, June 2, 2008.
Topology Seminar, The University of Texas at Austin, January 28, 2008.
Joint Postdoc Seminar, Mathematics Sciences Research Institute, October 19 2007.
Group Actions Seminar, Yale University, October 16, 2006.
Student Seminar (exposition), Yale University, May 1, 2004.