Research

Papers, talks, and activities

Published papers

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

31. Sang-hyun Kim and Thomas Koberda. Non-freeness of groups generated by two parabolic elements with small rational parameters. Michigan Mathematical Journal (2022) [pdf] [journal]

For a rational number q = s / r in (-4, 4), consider two 2 x 2 matrices a = ( (1, 0), (1, 1) ) and b = ( (1, q), (0, 1) ). We prove that the group < a , b > is non-free if s ≤ 27 and s ≠ 24. If s = 24, we prove the same statements for almost all r in the sense of natural density. We give an estimate for such a density when s > 27. Some of the proofs are computer-assisted, the output of which is given below.

Ancillary file of the above paper for the computer--assisted proofs

30. Sang-hyun Kim and Genevieve Walsh. Some groups with planar boundaries, Surveys in Differential Geometry (2022). [PDF] [journal]

We give an illustration of Bowditch's canonical splitting of one-ended hyperbolic groups, as well as a survey on the planarity conjecture regarding the Gromov boundary of a hyperbolic group.

29. Sang-hyun Kim, Thomas Koberda and Cristóbal Rivas. Virtual critical regularity of mapping class group actions on the circle, Transformation Groups (2022) [PDF] [journal]

We prove that if G and H are nonsolvable groups then (G x H) * Z does not embed into the group of the orientation preserving C^{1+t} diffeomorphisms of the circle for any t > 0. It follows that no finite index subgroup of the mapping class group of a closed hyperbolic surface can faithfully act on the circle by C^{1+t} diffeomorphisms, for any t > 0.

28. Sang-hyun Kim and Thomas Koberda. Structure and regularity of group actions on one-manifolds, 285 pages, Springer Monographs in Mathematics (November 21, 2021). [pdf] 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. [pdf] https://doi.org/10.3934/jmd.2021009

We prove that if G and H are nonsolvable groups then (G x H) * Z does not embed into the group of the orientation preserving C^{1+t} diffeomorphisms of the interval for any t > 0.

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) [pdf] https://doi.org/10.1007/s00209-021-02745-3

We study the question of how often the monodromy image of a once-punctured torus with a fixed irrational cone angle becomes a free group.

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. doi: 10.3934/dcds.2020259

We prove that if α(x)​​ is a concave modulus such that 1/α(x)​ is integrable near zero, then there exists a C1,α​​ diffeomorphism of the circle with an exceptional minimal set. We also generalize this to groups with polynomial growth, and deduce a partial converse. 

24. Chritian 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. DOI: 10.2140/agt.2020.20.3183 [pdf]

For a compact Riemannian manifold M and for a finitely generated group G = H ⧕ < t > with a hyperbolic linear action of t on H^1(H, ℤ), every C¹--action of G on M that is sufficiently close to the trivial action has an abelian image. As an example, we deduce the same conclusion when G is a fibered 3-manifold group.

23. Sang-hyun Kim and Thomas Koberda. Diffeomorphism groups of critical regularity. Inventiones mathematicae , 221(2), 421-501 (2020). [pdf] [journal page]

We prove that for each real numbers a ≥ 1, there exists a finitely generated subgroup Ga of Diffa(S1) with the property that Ga admits no injective homomorphisms into Diffb(S1) for all b > a. We also prove that there exists another fg group Ha that embeds into Diffb(S1) for all b < a, but not into Diffa(S1). One can further require the same properties are inherited to all finite index subgroups and to the commutator groups of Ga and of Ha. The commutator groups will be simple.

22. Sang-hyun Kim, Thomas Koberda and Mahan Mj, Flexibility of Group Actions on the Circle, Springer Lecture Notes in Mathematics 2231 (2019). [journal page] [Amazon page]

We study which finitely generated groups admit uncountably many pairwise-non-conjugate embeddings into PSL(2,R). In particular, we obtain a combination theorem of such a class of groups, encompassing free product and HNN extensions, both amalgamated over maximal abelian subgroups.

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. [Link]

We study subgroups of Homeo(R) generated by finitely many homeomorphisms each of which is supported on a single interval. As a consequence, we construct uncountably many non-pairwise isomorphic countable simple orderable groups.

20. Hyungryul Baik, Sang-hyun Kim and Thomas Koberda. Unsmoothable group actions on compact one-manifolds, doi: 10.4171/JEMS/886, Journal of European Mathematical Society, Volume 21, Issue 8, 2019, pp. 2333–2353. Published 16 April 2019.

Let G be the mapping class group of a surface (possibly with punctures or boundary), such that G is not virtually free. We prove that G never admits, even virtually, an embedding into the C1+bv diffeomorphism group of the circle.

19. Sang-hyun Kim and Thomas Koberda. Free products and algebraic structures of diffeomorphism groups, Journal of Topology, Volume11, Issue4, December 2018, Pages 1053-1075. https://doi.org/10.1112/topo.12079

We prove that if a finitely generated group G is not virtually abelian, then (G x Z) * Z never admits an embedding into the C1+bv diffeomorphism group of a compact one-manifold. As a consequence, we have a complete classification of RAAGs that embed into Diffr(S1) for each 0 ≤ r ≤  ω. (The cases r ≤ 1 and r = ω were previously known)

18. Sang-hyun Kim. Surface subgroups of word-hyperbolic groups (survey), Handbook of group actions. Vol. III, 89-102, Adv. Lect. Math. (ALM), 40, Higher Education Press and International Press, Beijing-Boston. Book chapter

We survey known results on Gromov's question regarding surface subgroups of word-hyperbolic groups.

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

We give an exposition on embeddability results related to RAAGs (right-angled Artin groups) and various automorphism groups of manifolds.

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. Published

We compute Lagrangian Floer potentials for Seidel Lagrangians on hyperbolic 2--orbifold spheres.

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. Published

We prove that every RAAG embeds into the C∞ diffeomorphism group of the real line.

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.

Let S be a surface with the complexity xi(S) < 3. We prove that if a RAAG A(X) embeds into Mod(S), then X must appear in the curve graph C(S) as an induced subgraph. We also give counterexamples for xi(S)>3.

13. Sang-hyun Kim and Thomas Koberda. Anti-trees and right-angled Artin subgroups of braid groups, Geometry & Topology 19-6 (2015), 3289--3306. DOI 10.2140/gt.2015.19.3289 Published

We prove that every RAAG (right-angled Artin group) embeds into some RAAG defined by an anti-tree. As a consequence, every RAAG embeds into some braid group, and also into Symp(S2) by a quasi-isometry with word-- or Lp--metric for p>2; this strengthens M. Kapovich's result.

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

We prove that a combinatorial triangulation L of S2 can be realized as an acute geodesic triangulation if and only if L does not have a separating three- or four-cycle.

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. Published

We develop a theory of right-angled Artin group actions on extension graphs, which parallels mapping class group actions on curve graphs. In particular, we concretely compute an acylindricity constant of the action.

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. Published

We prove that the double of a rank-two free group either splits as a nontrivial free product or contains a closed hyperbolic surface subgroup.

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. Published

We prove that a large chromatic number of the defning graph is an obstruction for a RAAG to embed into a given mapping class group.

8. Sang-hyun Kim and Thomas Koberda. Embeddability between right-angled Artin groups, Geometry & Topology 17 (2013) 493--530. [Link]

We propose that a notion of ``extension graph can be used for a systematic study of embedability between two RAAGs.

7. Sang-hyun Kim and Henry Wilton. Polygonal words in free groups, Quarterly Journal of Mathematics (2012) 63(2), 399--421. Published

We define a combinatorial group theoretic notion ``polygonality, and show that this notion can be used to find surface subgroups in many (conjecturally, all) doubles of free groups.

6. Sang-hyun Kim. Surface subgroups of graph products of groups, International Journal of Algebra and Computation (2012) 22 (8). Published

For a graph product G of groups {Gi}, we study the kernel K of the map G -> ∏i Gi. We show K embeds into some RAAG. When each Gi is finite or cyclic, then G is virtually special. We deduce that when X is a graph with up to seven vertices, then the right-angled Coxeter groups on X contains a hyperbolic surface subgroup if and only if X is weakly chordal.

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

We prove that ``geometric words (defined by Gordon--Wilton) are polygonal, as defined in [5].

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

We prove a combination theorem for the family of RAAGs that do not admit ``relative embedding of surface groups.

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), June 21-24, 2009 (Perugia, Italy) (2009).

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), Special Issue on Managing Complexity in Multiuser MIMO Systems, vol. 3, no. 6 (2009) 1094--1105.

1. Sang-hyun Kim. Co-contractions of graphs and right-angled Artin groups, Algebraic and Geometric Topology 8 (2008) 849--868. Published

We prove the injectivity of a map between RAAGs, which comes from a graph operation called co-contraction. A family of words that yield such embeddings, called contraction words, is also described.

submitted or accepted papers

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

We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. We also establish an analogous result for closed subgroups of locally compact groups. Our results are based on an earlier result of U. Hamenst\"{a}dt regarding finitely, and recover a theorem by Deroin, Kleptsyn and Navas regarding one-manifolds. 

4. Sang-hyun Kim, Nicolás Matte Bon, Mikael de la Salle and Michele Triestino, Subexponential growth and C1 actions on one-manifolds. [ArXiv]

We prove that if a countable group does not contain a finitely generated subgroup of exponential growth, then every topological action of the group on a compact connected one-manifold can be blown-up to a C1 action. The proof is based on a functional characterisation of such groups.

3. Sang-hyun Kim, Thomas Koberda and Javier de la Nuez-Gonzalez. First order rigidity of homeomorphism groups of manifolds. [Link] [ArXiv]

We prove that every compacted connected manifold M admits a purely group theoretic first order sentence "I-am-M" in its homeomorphism group, and also in its measure-preserving homeomorphism group. Consequently, these groups are first order rigid among the (measure-preserving) homeomorphism groups of compact connected manifolds.

2. 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). [Link]

We prove that if n is a prime or its square then the congruence subgroup Gamma_0(n) admits a freely independent set of generators whose (2,1) components are exactly 0 or n.

1.  Jaewon Chang, Sang-hyun Kim and Thomas Koberda. Algebraic Structure of Diffeomorphism Groups of One--Manifolds (accepted, Vol 84 of Panoramas et Synthèses by SMF)

Mather proved that the group of Ck --diffeomorphisms of an n--manifold is simple, provided that a mild isotopy condition is satisfied, with the possible exception of k=n+1$. We give a detailed account of Mather's proof in the case when n=1 and extend this result to a slightly larger class of diffeomorphism groups of certain ``tame regularities.

unpublished notes

1. (With Thomas Koberda and Juyoung Lee), Finite subgraphs of extension graphs.

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.

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

Upcoming

1. Conference (TBA), June 17, 2025, BICMR

Complete

2. East Asian Conference on Geometric Topology 20, Tokyo, Japan, February 4, 2025.

3. Friday Seminar on Knot Theory, OCAMI, Osaka, Japan, January 31, 2025.

4. What is...? (on rotation number), Osaka University, Japan, January 30, 2025.

5. 2025 KMS-VMS Joint Workshop, Hanoi, Vietnam, January 6 - 10, 2025.

6. Geometry and Dynamics in Low-Dimensions, Hanoi, Vietnam, Janury 6 - 10, 2025.

7. On Dream Young Mathematicians Camp (for high school students), January 5, 2025.

8. Topology Seminar, National University of Singapore, December 26, 2024.

9. Foliations and Diffeomorphism Groups, CIRM, Marseille, December 9 - 13, 2024.

10. Dynamical Group Theory V (KOREA: KIAS workshop on One RElator groups and other Aspects of GGT), September 27, 2024. [Link]

11. KAIST, Basic Science Week, October 30, 2024.

12. Davinci Motel by Hyundai Card (public talk), Seoul, September 28, 2024.

13. Dynamical Group Theory IV (KIAS-Rice Workshop), September 27, 2024. [Link]

14. Public Lecture, Huh June Center for Mathematical Challenges, September 7, 2024. [Link]

15. Colloquium, Huh June Center for Mathematical Challenges, September 5, 2024.

16. Public Lecture organized by Korea Academy of Science and Technology (KAST), Seoul Science High School, August 19, 2024.

17. Panel Discussion, World Congress of Korean and Korean-Ethnic Scientists and Engineers, Seoul, July 11, 2024.

18. KFAS Summer 2024, Gangneung, Korea, July 4 - 6, 2024.

19. KAOS Science, "100 years of geometric topology and the Poincaré conjecture", July 3, 2024
    [Stream Link] (recording: June 17)

20. REU Colloquium, University of Virginia, June 19, 2024 (8 PM, US EST) / June 20, 2024 (9 AM, KST) : online.

21. Computational aspects of thin groups, Institute for Mathematical Sciences National University of Singapore, June 11, 2024.

22. An-ahm Lecture, Korea University, May 20, 2024

23. Low Dimensional Actions, IHP (Institute Henri Poincaré), Paris, April 29 - May 3, 2024. [Link]

24. Oberseminar Differentialgeometrie, Max Planck Institute for Mathematics, April 25, 2024. [Link]

25. Special Session on Geometric Structures and Representation Spaces, Korean Mathematical Society , KAIST, Daejeon, April 20, 2024. 

26. Colloquium, KRIMS, Kangwon University, April 17, 2024.

27. Math Colloquium, Postech, Pohang, March 22, 2024. [Link]

28. The 19th East Asian Conference of Geometric Topology, Kyoto, Japan, February 19 - 23, 2024.

29. KAIST Geometric Topology Fair 2024, Busan, Jan 15 - 19, 2024

30. Round table discussion on publicizing science culture, Ministry of Science and ICT, Korea, January 10, 2024, [news]

31. "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]

32. Department Colloquium, Yonsei University, Seoul, Korea, November 9, 2023 (5 pm).

33. Dream Lecture Series by Korea Foundation for Advanced Studies, West Daejeon Highschool, Oct 18, 2023.

34. The 4th Korea-France Conference in Mathematics, August 21 - 25, 2023, KIAS, Korea.

35. 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).

36. Characters and Moduli of Surfaces (SerFest), The Research Institute for Mathematical Sciences (RIMS), Kyoto, Japan, July 19 - 21, 2023.

37. The Mathematical Society of Japan -- Seasonal Institute (MSJ-SI), New aspects of Teichmüller theory, University of Tokyo, Japan, July 9 - 15, 2023.

38. Korea Foundation for the Advancement Science & Creativity, International Olympiad Team Ceremony, June 14, 2023.

39. NCTS 2023 dynamics workshop (minicourse of 3 talks), National Center for Theoretical Sciences (NCTS), National Taiwan University, Taiwan, June 8-10, 2023.

40. Topology Seminar, Gakushuin University, May 26, 2023.

41. Special Session on Geometric Structures and Representation Spaces, Korean Mathematical Society , April 28, 2023. 

42. Topology seminar, Seoul National University, April 21, 2023. 

43. The 3rd Probabilistic Methods in Negative Curvature workshop  (minicourse of 4 talks), ICTS Bangalore, India, February 27 -- March 10, 2023 (mini-course).

44. Conformal dynamics and groups, BICMR, December 2, 2022 (online).

45. The Pacific Rim Mathematical Association Congress 2022 (PRIMA CONGRESS 2022), Vancouver, Canada, Special Session on ``Geometric Group Theory'', December 2022 (TBD).

46. School on Dynamical Group Theory, Dijon, France, Oct 3 - 7, 2022 (mini-course of 3 talks).

47. Mathematics Department Colloquium, Sookmyung Women's University, September 15, 2022.

48. REU Colloquium, University of Virginia, July 27, 2022 (US EST) / July 28, 2022 (KST) : online.

49. Topology and Geometry Seminar, National University of Singapore, July 4, 2022.

50. Regular Workshop, Integrative Research Institute in Basic Science, Soongsil University, June 24, 2022.

51. Geometry and Analysis on Groups Research Seminar, University of Vienna, June 7, 2022. 

52. OpenKIAS Public Lecture, Korean Mathematical Society, April 28, 2022 (5pm), hybrid.

53. "공간의 풍경 (The landscape of a space), KIAS Public Lecture, Korean Mathematical Society Spring Meeting, April 28, 2022. [Youtube]

54. Sydney Mathematical Research Institute (SMRI) Algebra and Geometry Online seminar, March 2nd, 2022 (Wed, 11 am KST/ 1 pm Australia). [youtube]

55. Future intelligence (forum), CHUNG MONG-KOO Foundation and Chosun Ilbo, February 17, 2022. [youtube] [youtube (sketch)] [news article]

56. Samsung Sciences & Technology Foundation Annual Forum, November 22, 2021.

57. Geometry and Topology Online, Warwick Mathematics Institute, November 18, 2021 (online).

58. Human, Mathematics, Computer (On the Halting problem of Turing), KFAS building, Dream Lecture Series by Korea Foundation for Advanced Studies, November 13, 2021.

59. Symmetry in Newcastle (seminar), The University of Newcastle, Australia, November 1, 2021 (online). [youtube]

60. Graduate seminar on mathematical challenges, Yonsei University, October 6, 2021.

61. VI Congreso Latinoamericano de Matemáticos (CLAM) 2021, Montevideo, Uruguay, September 14, 2021 (online).

62. REU Colloquium, University of Virginia, July 21, 2021 (online).

63. Mathematical Sciences Department colloquium, Seoul National University, May 6, 2021. "On Circle Diffeomorphism Groups" (online).

64. The 16th East Asian Conference on Geometric Topology, University of Tokyo, Japan, January 25, 2021. (online, invited talk)

65. OpenKIAS public lecture - 불가능에 대하여 (갈루아, 괴델, 튜링, 힐버트), December 22, 2020. [Youtube]

66. Expanding Dynamics, CMM - Center for Mathematical Modeling / Universidad de Chile, October 13, 2020. (online)

67. Teichmüller Theory: Classical, Higher, Super and Quantum, CIRM, Luminy, France, October 8, 2020. (online)

68. The 3rd International Undergraduate Mathematics Summer School, Seoul National University,TBD, 5 lectures, postponed.

69. Mathematics Colloquium, Seoul National University, Korea, TBD. Groups of circle diffeomorphisms: analysis, dynamics and algebra, postponed.

70. 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

71. REU Colloquium, University of Virginia, June 24, 2020 (online).

72. Colloquium at Electrical Engineering School, DGIST, Korea, June 2, 2020 (online).

73. Hyperbolic Lunch, University of Toronto, May 13, 2020. (online)

74. Virtual Seminar on Geometry and Topology (visgat), KIAS and KAIST, March 31, 2020. (online)

75. Topology Seminar, Gakushuin University, December 2, 2019.

76. Mathematics Colloquium, KAIST, November 21, 2019.

77. Mathematics Colloquium, Korea University, November 15, 2019.

78. Arbeitsgemeinschaft: Zimmer's Conjecture, Mathematisches Forschungsinstitut Oberwolfach, Germany, 13 -- 18 October, 2019. Title: Property T and actions on S^1.

79. Geometry and Analysis on Groups Seminar, University of Vienna, Austria, October 8, 2019.

80. Summer School on Geometric Topology and Algebraic Geometry, KAIST, Korea, August 12 an 13, 2019.

81. 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.

82. Ordered Groups and Rigidity in Dynamics and Topology, Oaxaca, Mexico, June 17, 2019.

83. Undergraduate seminar, Kwangwoon University, June 7, 2019.

84. 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.

85. Ergodic and Geometric Group (EGG) Theory seminar, EPFL, Lausanne, Swiss, May 27, 2019.

86. Non-positive curvature, Warsaw, Poland, May 20, 2019.

87. Geometry and Analysis on Groups Seminar, University of Vienna, Austria, May 16, 2019.

88. Public lecture at Mathematics Culture Festival, Gwachun National Science Museum, Korea, April 27, 2019.

89. Public lecture (organized by The Korean Academy of Science and Technology), Yeongnam High School, Daegu, Korea, April 3, 2019.

90. Special Sessions on Mapping Class Groups, University of Hawaii at Manoa, Honolulu, US, March 23, 2019.

91. The 14th East Asian Conference of Geometric Topology, Beijing, China, January 23, 2019. (plenary)

92. Suzhou 2019 Workshop on Geometry Topology, Soochow University, Suzhou, China, January 18, 2019.

93. Boundaries of topological groups, C*-algebras, symmetric spaces, and Lyapounov exponents, TSIMF, Sanya, China, December 20, 2018.

94. One-day Workshop about Dynamics, Geometry and Groups, Suwon, Korea, December 5, 2018.

95. KIAS Analysis Seminar, Seoul, Korea, November 1, 2018.

96. New Trends in Teichmüller Theory and Mapping Class Groups, Mathematisches Forschungsinstitut Oberwolfach, Germany, September 2--8, 2018.

97. Department Seminar, Chiang Mai University, Thailand, August 24, 2018.

98. Talk concert (for general public), Gwachun National Science Museum, Korea, Aug 19, 2017.

99. Science Camp, College of Natural Sciences, Seoul National University, (1) August 3, 2016 (2) August 9, 2018.

100. International Conference on Dynamical Systems, Sustech, China, June 25--28, 2018. Slide (PDF)

101. Hyperbolic 3-manifolds and related topics, Postech, Korea, June 18-- 22, 2018.

102. Silk Road Geometry Conference, Gokova Geometry/Topology Institute (GGTI), Turkey, June 4 - 8, 2018.

103. Dream Lecture Series by Korea Foundation for Advanced Studies, Hanyoung Foreign Language High School, May 14, 2018.

104. Dream Lecture Series by Korea Foundation for Advanced Studies, KFAS building, May 12, 2018.

105. Topology in Australia and South Korea, IBS-CGP, Korea, April 25--27, 2018.

106. KIAS (Korea Institute for Advanced Study), Korea, April 17, 2018.

107. Topology Seminar, KAIST, Korea, March 27, 2018.

108. Branched Coverings, Degenerations, and Related Topics 2018 (minicourse), Hiroshima University, Japan, March 5 - 9, 2018.

109. Structure of 3-manifold Groups, CIRM (Luminy), France, February 26 - March 2, 2018.

110. Workshop on Geometric Group Theory (minicourse), BICMR, Beijing University, December 16 - 17, 2017.

111. Kyoto University, December 12, 2017.

112. Low-dimensional topology seminar, Osaka University, December 5, 2017.

113. Topology Seminar, University of Tokyo, November 28, 2017.

114. Max Dehn Seminar, University of Utah, October 25, 2017.

115. Topology Seminar, Rice University, October 23, 2017.

116. Topology Seminar, University of Texas at Austin, October 20, 2017.

117. Colloquium, University of Virginia, October 12, 2017.

118. Geometric Group Theory and Topology Seminar, Tufts University, October 3, 2017.

119. Geometry and Topology Seminar, Brown University, September 29, 2017.

120. GGT Seminar, MgGill University, September 27, 2017.

121. Japan Conference on Discrete and Computational Geometry, Graphs, and Games: JCDCG3, Tokyo University of Science (Aug 29 - Sep 1), Tokyo, Japan, August 29, 2017.

122. Japanese Topology Symposium, Tokai University, Tokyo, Japan, August 21 -- 24, 2017, 2017.

123. Invited talk, Korea Institute for Advanced Study (KIAS), Korea, Aug 7, 2017.

124. Dream Lecture Series by Korea Foundation for Advanced Studies, KFAS building, July 15, 2017.

125. GAGTA 2017: Geometric and Asymptotic Group Theory with Applications (July 3 -- 7), Bilbao, Spain, July 4, 2017.

126. SFB Seminar, Universität Regensburg, Germany, June 30, 2017.

127. Séminaire Géométrie, Dynamique et Topologie (GDT), L’Institut de Mathématiques de Marseille (I2M), France, May 22, 2017.

128. Geometry Seminar, ETH Zürich, Swiss, May 3, 2017.

129. Ergodic and Geometric Group (EGG) Theory seminar, EPFL, Lausanne, Swiss, April 27, 2017.

130. Thursday Colloquium, TIFR, Mumbai, India, April 20, 2017.

131. IBS--CGP Seminar, Pohang, Korea, April 13, 2017.

132. Department Colloquium, Sungkyunkwan University, Suwon, Korea, April 6, 2017.

133. Dream Lecture Series by Korea Foundation for Advanced Studies, Young-rak High School, March 20, 2017.

134. Topology--Geometry Seminar, Hiroshima University, Japan, March 16, 2017.

135. Topology Seminar, Osaka University, Japan, March 13, 2017.

136. Young Mathematicians' Camp, National Institute for Mathematical Sciences, Daejeon, February 22, 2017.

137. SNU Geometry and Topology Mini-Workshop, Seoul National University, Korea, February 17, 2017.

138. College of Natural Sciences Public Lecture, Seoul National University, Korea, February 9, 2017. [youtube]

139. SNU Topology Winter School, December 16,, 2016.

140. Virginia Topology Conference, University of Virginia, November 18, 2016.

141. Geometry and Topology Seminar, Seoul National University, November 16, 2016.

142. Topology Seminar, Sungkyunkwan University, November 15, 2016.

143. Invited Talk, Korean Mathematical Society Annual Fall Conference, October 22, 2016.

144. Dream Lecture Series by Korea Foundation for Advanced Studies, Seoul High School, October 14, 2016.

145. 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.

146. Dream Lecture Series by Korea Foundation for Advanced Studies, KFAS building, July 23, and July 30, 2016.

147. Geometric Topology Fair 2016, KAIST, Daejeon, July 7, 2016.

148. GAGTA (Geometric and Asymptotic Group Theory and Applications) 2016, Stevens Institute of Technology, June 17, 2016.

149. IBS--CGP seminar, IBS--CGP, Pohang, Korea, April 21, 2016.

150. Saturday Public Science Lectures, College of Natural Sciences, Seoul National University, March 26, 2016.

151. Mathematics seminar, Konkuk University, Seoul, Korea, March 25, 2016.

152. Invited lecture, Korea Institute for Advanced Study (KIAS), Korea, Mar 2, 2016.

153. Group actions seminar, Yale University, Feb 22, 2016.

154. Geometry and topology seminar, Univ. of Massachusetts at Amherst, Feb 19, 2016.

155. Geometric group theory seminar, Tufts University, Feb 18, 2016.

156. Teichmüller theory and low-dimensional topology, Tsinghua Sanya International Mathematics Forum (TSIMF), China, Jan 11 - 15, 2016. script

157. East Asian Conference on Algebraic Topology 6 (EACAT-6), Daejeon, November 30 - Dec 4, 2015.

158. 2015 International Workshop on Mathematical Sciences in Dalian, China, Oct 30 - Nov 1, 2015.

159. Saturday Public Science Lecture, College of Natural Sciences, Seoul National University, Oct 24, 2015.

160. Department Colloquium, Ewha Women's University, Oct 15, 2015.

161. University of Rennes, France, October 1, 2015.

162. Dream Lecture Series by Korea Foundation for Advanced Studies, Chil-won High School - October 16, 2015.

163. Dream Lecture Series by Korea Foundation for Advanced Studies, Seo-oon Middle School - September 4, 2015.

164. IBS--CGP Mathematics Festival for Undergraduates, Aug 17 - 21, 2015. script

165. Dubrovnik VIII - Geometric Topology, Geometric Group Theory and Dynamical Systems, Croatia, June 22 - 26, 2015.

166. Statistics seminar, Seoul National University, Korea, June 4, 2015.

167. Dream Lecture Series by Korea Foundation for Advanced Studies, Seocho High School - May 29, 2015.

168. Dream Lecture Series by Korea Foundation for Advanced Studies, Kyungshin High School - May 8, 2015.

169. Geometry & Topology seminar, Postech, Korea, April 22, 2015.

170. Geometric Group Theory on Gulf Coast (G^3), San Padres Island, USA, March 26 - 29, 2015. 

171. KIAS Algebra Seminar, KIAS, January 5, 2015.

172. Dream Lecture Series by Korea Foundation for Advanced Studies, KFAS building, December 20, 2014.

173. Group Action Forum, Tsinghua Sanya International Mathematics Forum, China, December 15 -- 19, 2014.

174. KIAS/CMC Colloquium, KIAS, December 2, 2014.

175. Department Colloquium, Chiang Mai University, October 28, 2014.

176. Dream Lecture Series by Korea Foundation for Advanced Studies, Banpo High School, September 13, 2014.

177. 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. script

178. Discrete Groups and Geometric Structures with Applications V, KU Leuven, Belgium, June 2 - 6, 2014.

179. Seoul National University Department Colloquium, Subgroups of Mapping Class Groups, March 13, 2014

180. Branched Coverings, Degenerations, and Related Topics 2014, Hiroshima University, Japan, March 7, 2014.

181. Groups and Geometry in the South East, Mathematics Institute, Warwick University, United Kingdom, February 21, 2014.

182. Complex Analysis and Topology of Discrete Groups and Hyperbolic Spaces, Research Institute for Mathematical Sciences, Kyoto University, Japan, January 24, 2014.

183. 5th East Asian Conference of Algebraic Topology (EACAT 5), Chinese Academy of Sciences, Beijing, China, December 3, 2013.

184. Wasatch Topology Conference, the University of Utah, USA, November 16, 2013.

185. Topology Seminar, University of Texas at Austin, November 11, 2013.

186. Geometry and Topology Seminar, City University of New York, November 5, 2013.

187. Discovery-oriented class in calculus, Inha University Pedagogy Workshop, October 28, 2013. script

188. Korean Mathematical Society Annual Meeting, University of Seoul, Korea, October 25, 2013.

189. Geometry and Topology Seminar, Brown University, October 9, 2013.

190. Topology/Geometry Seminar, Yale University, October 8, 2013.

191. New York Applied Algebra Colloquium, City University of New York, 27 September, 2013.

192. Geometric and Analytic Group Theory, Ventotene Island, Italy, September 9-14, 2013.

193. Geometric Structures on Low-Dimensional Manifolds, Korea Institute for Advanced Study, Korea, May 24, 2013.

194. Discrete Math Seminar, KAIST, April 19, 2013.

195. Hot Topics: Surface subgroups and cube complexes, Mathematical Sciences Research Institute, USA, March 19, 2013.

196. Topology and Geometry Seminar, National University of Singapore, February 13, 2013.

197. Geometric Group Theory and Topology Seminar, Tufts University, January 29, 2013.

198. Topology/Geometry Seminar, Yale University, January 22, 2013.

199. Manhattan Algebra Day, Stevens Institute, USA, December 7, 2012.

200. Topology Seminar, Osaka University, December 4 2012.

201. Friday Workshop on Geometry of Artin Groups, KIAS, November 23, 2012.

202. Topology Seminar, Hanyang University, October 19 and October 26, 2012.

203. Department Colloquium, Sogang University, October 18 2012.

204. MSJ-KMS Joint Meeting, Kyushu University, Japan, September 17, 2012. script

205. Topology Seminar, KAIST, September 5 2012.

206. The 10th KAIST Geometric Topology Fair, KAIST, Daejeon, Korea, August 16, 2012.

207. Geometric and Asymptotic Group Theory with Applications (GAGTA-6), University of Duesseldorf, July 30, 2012.

208. Geometric Group Theory - Kyoto 2012, Kyoto University, Japan, June 7, 2012.

209. Department Colloquium, Ulsan University, April 12 2012.

210. 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. script

211. Geometry and Topology Seminar, SUNY Buffalo, January 25, 2012.

212. AMS-MAA Joint Meeting, Special session on hyperbolicity in manifolds and groups, Boston, January 4, 2012.

213. Department Colloquium, Konkuk University, Seoul, Korea, November 17, 2011.

214. Department Colloquium, Hanyang University, Seoul, Korea, November 4, 2011.

215. Department Colloquium, Yonsei University, Seoul, Korea, October 13, 2011.

216. Department Colloquium, Seoul National University, Seoul, Korea, September 29, 2011.

217. The 4th Topology Workshop, Chonbuk National University, Jeonju, Korea, August 23 - 24, 2011.

218. The 9th KAIST Geometric Topology Fair, KAIST, Daejeon, Korea, August 9, 2011.

219. Geometric and Asymptotic Group Theory with Applications (GAGTA--5), Universitat Politecnica de Catalunya, Barcelona, Spain, July 12, 2011.

220. Dubrovnik VII - Geometric Topology, Inter-University Centre and University of Zagreb, Dubrovnik, Croatia, July 2, 2011.

221. Geometry/Topology Seminar, University of Chicago, April 12, 2011.

222. Topology/Geometry Seminar, Yale University, April 5, 2011.

223. Spring Topology and Dynamics Conference, University of Texas at Tyler, U.S.A., March 18, 2011.

224. AMS Southeastern Section Meeting, Special Session on Geometric Group Theory, Georgia Southern University, U.S.A., March 13, 2011.

225. Topology and Geometric Group Theory Seminar, Cornell University, March 8, 2011.

226. Bernstein Seminar, Cornell University, March 8, 2011.

227. AMS-MAA Joint Meeting, Special session on groups, geometry and applications, New Orleans, January 7, 2011.

228. Topology Seminar, KAIST, Korea, December 23, 2010.

229. Geometry and Topology Seminar, SUNY Buffalo, November 19, 2010.

230. Topology Seminar, University of Texas at Austin, November 8, 2010.

231. Geometry and Topology Seminar, Caltech, October 22, 2010.

232. Approaches to Group Theory, Using Algebraic, Analytic, and Geometric Tools in the Study of Groups, Cornell University, U.S.A., October 10, 2010.

233. Topology Seminar, Brandeis University, September 21 2010.

234. Geometric Group Theory and Topology Seminar, Tufts University, September 14, 2010.

235. KAIST Topology Workshop, Daejeon, Korea, August 4, 2010.

236. KAIST--POSTECH--SNU YB Workshop, Jeonju, Korea, July 3, 2010.

237. Topology Seminar, University of California at Santa Barbara, May 18, 2010.

238. AMS Special Session on Geometric Group Theory, University of New Mexico, U.S.A., April 18 2010.

239. Geometric Group Theory Seminar, Tufts University, January 19, 2010.

240. BK21 Seminar, KAIST, January 26 2010.

241. Joint Topology and Discrete Math Seminar, KAIST, December 28, 2009.

242. Topology Seminar, Konkuk University, December 22, 2009.

243. 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.

244. Topology/Geometry Seminar, Yale University, October 27, 2009.

245. Topology Seminar, The University of Texas at Austin, August 31, 2009.

246. International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory, the University of Nebraska-Lincoln, U.S.A., May 20, 2009.

247. AMS Special Session on Recent Progress in Geometric Group Theory, San Francisco State University, April 25, 2009.

248. Topology Seminar, The University of Texas at Austin, April 13, 2009.

249. Groups and Dynamics Seminar, Texas A&M University, March 25, 2009.

250. Topology Seminar, The University of Texas at Austin, October 27, 2008. script

251. Groups and Infinite Graphs, Erwin Schroedinger International Institute, Austria, August 26, 2008.

252. Topology Seminar, Seoul National University, Korea, June 2, 2008.

253. Topology Seminar, The University of Texas at Austin, January 28, 2008. script

254. Joint Postdoc Seminar, Mathematics Sciences Research Institute, October 19 2007.

255. Group Actions Seminar, Yale University, October 16, 2006.

256. Student Seminar (exposition), Yale University, May 1, 2004. script

Activities

Positions

• Professor, Korea Institute for Advanced Study, 2019 - present.

• Adjunct Professor (joint appointment), Department of Mathematical Sciences, KAIST , 2019 - present.

• Seoul National University (Associate Professor), 2014 - 2018.

• KAIST (Assistant, Associate Professor), 2011 - 2014.

• Tufts University (Norbert Wiener Assistant Professor), 2010 - 2011.

• the University of Texas at Austin (R. H. Bing Instructor), 2008 - 2010.

• Mathematical Sciences Research Institute, 2007.

Students mentored

Hyunsu Park (SNU Master's 2016 - 2020)

Donggyun Seo (SNU PhD 2013 - 2020, KIAS Mar 2020 - Aug 2020)

Outreach

• Vietnam Polymath REU Program, Oct 2023 - Oct 2024 [Link]

  • REU Workshop at VIASM, July 2024.

• Great Minds, EBS : consulting for translating the five lectures of Professor Ian Stewart

Journals

• Editor, Journal of Korean Mathematical Society (2019 - ), [link]

• Editor, KIAS Springer Series in Mathematics (2021 - ), [link]
  Vol. 1. Recent Progress in Mathematics

• Editor, Horizon : a KIAS Webzine for promotion of science awareness in public (2022 - 2024), [intro] [link]

• Article reviews

- Reviewer, MR (Mathematical Reviews)

MR3033518 ; MR3125410 ; MR3158758 ; MR3158775 ; MR3668054 ; MR3728497 ; MR3738334 ; MR3797073 ; MR3858768 ; MR3864538 ; MR3909234 ; MR3954281 ; MR4009420 ; MR4020679 ; MR3993762

- Reviewer, zbMATH (Zentralblatt MATH)

Committee works

• KIAS Transdisciplinary Research, Program Committee, 2023 - present.

• KIAS Labor--Management Committee, KIAS, 2020 - present.

• Steering Committee, Center for Mathematical Challenges, KIAS, 2021 - present.

• Steering Committee, AI Center for Basic Sciences, KIAS, 2020 - present.

• Research Output Analysis Committee (성과분석위원), National Research Foundation of Korea (한국연구재단), 2020 - 2022.

• Review Board (전문위원, 분야별 지원체계 자문위원회), National Research Foundation of Korea  (한국연구재단), 2018 - present.

• Steering Committee, Seoul Science High School (2018.3 - 2020.2) 

• Topology Committee, Korean Mathematical Society (2023 - )

• Executive board member, Korean Mathematical Society (2013 - 2014)

• Member, Korean Mathematical Olympiad (KMO) Committee, 2013 - present (2023).

Conference Organization

Dynamical Group Theory (conference series) https://dgt.kimsh.kr

• Dynamical Group Theory V (KIAS workshop on One RElator groups and other Aspects of GGT), November 19 - 22, 2024.

• Dynamical Group Theory IV (KIAS-Rice Workshop), September 25 - 28, 2024.

• New Methods in Group Actions on Manifolds (Dynamical Group Theory III), August 13 - 16, 2024

• Korea-France Workshop on Dynamical Group Theory II (Korea-France Workshop), Feb 29, 2024. [Link]

• Korea-Chile Workshop on Dynamical Group Theory I (Korea-Chile Workshop), Incheon, Korea, September 27 - 28, 2023. [Link]

Organizing Committee

• Korean Mathematical Society Fall Meeting, Special Session on Geometric Group Theory, Oct 25-26, 2024.

• KIAS Graduate Student Meeting in Pure Mathematics, October 21st, 2024.

• Semigroups, groupoids and C*-algebras, July 1 - 5, 2024.

• Hyperbolic Geometry of Numbers, Dec 18 - 20, 2023. [Link]

• The 4th Korea-France Conference in Mathematics, KIAS, Seoul, Korea, August 21 - 25, 2023. [Link]

• Workshop on topological data analysis: mathematics, physics and beyond, KIAS, Korea, February 8 - 10, 2023

• PK² Topology Workshop http://cayley.kr/pk2

  • Fall 2022, Nov 1 - 4, 2022. Busan, Korea.

  • Spring 2022, May 29 - June 1, 2022. Jeju, Korea.

• The 6th Korea Toric Topology  Workshop, KAIST, Daejeon, Korea, July 11 - 13, 2022.

• East Asian Conference on Geometric Topology (EACGT 2022), Program/Organizing Committee, KIAS, Korea.

• One-dimensional actions of 3-manifold groups, Organizing / Scientific Committee, Dijon, France, November 4 - 8, 2019.

• Combinatorial and algebraic aspects of geometric structures, Chiang Mai University, Thailand, July 18 - 26, 2019.

• Scientific Committee / Organizer, GAGTA-2018, Seoul, Korea (2018)

• Organizer, IBS Undergraduate Mathematics Festival, 2015.

• Organizer, East Asian Conference on Algebraic Topology 6 (EACAT-6), Daejeon, Korea, 2015.

• Organizer, Geometric Group Theory Workshop, Seaes Hotel, Jeju Island, Korea Dates January 22 - 24,  2015.

• Organizer, Geometry on Groups and Spaces (ICM 2014 Satellite), Daejeon, Korea, 2014

• KAIST Geometric Topology Fair, 2011 - 2013 (annual)

Scientific / Steering / Program Committee

• GAGTA (Geometric and Asymptotic Group Theory with Applications), Steering Committee, 2023 - . [Link]

• Young Geometric Group Theory XII, Bristol, Scientific Committee, UK, 8 - 12 April 2024.

• GAGTA2023 (Geometric and Asymptotic Group Theory with Applications), Scientific Committee, Vienna, Austria, July 17 - 21, 2023.

• East Asian Conference of Geometric Topology, Program Committee, 2019 - present.

• yGGT-2024 (Bristol, UK),  yGGT-2019 (July 1 - 5, 2019, Bilbao, Spain), Scientific Committee.

• Workshop on Groups, Geometry and Dynamical System (ICM 2018 satellite), Scientific Committee, Montevideo, Uruguay (2018)

Teaching

Seoul National University

Algebraic Structure of Diffeomorphism Groups (graduaute course), Spring 2018. Dynamics on the Circle (graduate course), Spring 2016.

Geometry on Infinite Groups (graduate course), Fall 2014.

Mathematics and recitation 1, 2 (non-math majors Calculus), Spring and Fall 2014. Calculus 1 and 2 (math majors), Spring and Fall 2015, 2018.

Topology 1, 2 (undergraduate), Spring and Fall 2015. Mathematics for Biology 1, 2, Spring and Fall 2016. Algebraic Topology 1, Fall 2016, 2018.

KAIST

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 Education 3.0 Calculus I, Spring 2012, Spring 2013 – a discovery oriented course with bottom-up approach and multimedia integration.

Education 3.0 Calculus II, Fall 2012.

Algebraic Topology I (graduate course), Spring 2013.

Groups, Graphs and Geometry (graduate course), Spring 2012. Calculus II (Calculus of Several Variables), Fall 2011. Freshman Seminar, Fall 2011.

Tufts University

Calculus II, Fall 2010.

Calculus III, Fall 2010 and Spring 2011.

the University of Texas at Austin

Differential and Integral Calculus I, Spring 2008, Fall 2008 and Fall 2009. Differential and Integral Calculus II, Spring 2010.

Introduction to Number Theory, Summer 2009.

Probability I, Summer 2008 and Spring 2009.

Discrete Mathematics, Spring 2008.

Topics in Geometric Group Theory (graduate course), Spring 2010.

 Yale University

Calculus of Functions of One Variable, 2006 and 2007.

Introduction to Functions of Several Variables, 2006.

Calculus of Functions of Several Variables, 2001, 2002, 2003, 2004, 2005 and 2006.