Research (Sang-hyun Kim)

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Publications

Most papers by Sang-hyun Kim can be downloaded at http://arxiv.org/a/kim_s_3.

Published / to appear

16. (With Thomas Koberda and Yash Lodha), Chain groups of homeomorphisms of the interval and the circle, Annales Scientifiques de l'École Normale Supérieure, accepted.

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.

15. (With Hyungryul Baik and Thomas Koberda), Unsmoothable group actions on compact one-manifolds, accepted, Journal of European Mathematical Society.

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.

14. (With Cheol-Hyun Cho, Hansol Hong 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.

13. (With Hyungryul Baik and Thomas Koberda), Right-angled Artin subgroups of the C interval diffeomorphism group, June 2016, Volume 213, Issue 1, pp 175-182, Israel Journal of Mathematics. Published

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

12. (With Thomas Koberda), Right-angled Artin groups and finite subgraphs of curve graphs, Vol. 53 No.3, Osaka Journal of Mathematics (2016).

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.

11. (With 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.

10. (With Genevieve Walsh), Coxeter groups, hyperbolic cubes, and acute triangulations, Journal of Topology (2016) 9 (1): 117-142. doi: 10.1112/jtopol/jtv038 Published

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.

9. (With 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.

8. (With 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.

7. (With 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.

6. (With Thomas Koberda), Embedability between right-angled Artin groups, Geometry & Topology 17 (2013) 493--530. Published

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

5. (With 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.

4. 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.

3. 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].

2. 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.

1. 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.

Preprint

3. (With Thomas Koberda) Diffeomorphism groups of critical regularity

We prove that for each real numbers a ≥ 2, there exists a finitely generated subgroup Ga of Diffa(S1) such that Ga admits no injective homomorphisms into Diffb(S1) for all b > a. One can further require the same property for all finite index subgroups of Ga, and also for [Ga,Ga], which is a simple group.

2. (With Thomas Koberda), Free products and algebraic structures of diffeomorphism groups

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)

1. (With Thomas Koberda and Mahan Mj), Rotation spectra and exotic group actions on the circle

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.


Conference proceedings / surveys / other writings

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.


Publication: related area

2. Chan-Byoung Chae, Sang-hyun Kim (2nd author) 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).

1. Chan-Byoung Chae, Sang-hyun Kim (2nd author) 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.


Research Talks

This is the list of the talks by Sang-hyun Kim.

2018

  1. Silk Road Geometry Conference, Gokova Geometry/Topology Institute, June 4 - 8, 2018.
  2. Branched Coverings, Degenerations, and Related Topics 2018 (minicourse), Hiroshima University, Japan, March 5 - 9, 2018.

2017

  1. Workshop on Geometric Group Theory (minicourse), BICMR, Beijing University, December 16 - 17, 2017.
  2. Kyoto University, December 12, 2017.
  3. Low-dimensional topology seminar, Osaka University, December 5, 2017.
  4. Topology Seminar, University of Tokyo, November 28, 2017.
  5. Max Dehn Seminar, University of Utah, October 25, 2017.
  6. Topology Seminar, Rice University, October 23, 2017.
  7. Topology Seminar, University of Texas at Austin, October 20, 2017.
  8. Colloquium, University of Virginia, October 12, 2017.
  9. Geometric Group Theory and Topology Seminar, Tufts University, October 3, 2017.
  10. Geometry and Topology Seminar, Brown University, September 29, 2017.
  11. GGT Seminar, MgGill University, September 27, 2017.
  12. Japan Conference on Discrete and Computational Geometry, Graphs, and Games: JCDCG3, Tokyo University of Science (Aug 29 - Sep 1), Tokyo, Japan, August 29, 2017.
  13. Japanese Topology Symposium, Tokai University, Tokyo, Japan, August 21 -- 24, 2017, 2017.
  14. Invited talk, Korea Institute for Advanced Study (KIAS), Korea, Aug 7, 2017.
  15. GAGTA 2017: Geometric and Asymptotic Group Theory with Applications (July 3 -- 7), Bilbao, Spain, July 4, 2017.
  16. SFB Seminar, Universität Regensburg, Germany, June 30, 2017.
  17. Séminaire Géométrie, Dynamique et Topologie (GDT), L’Institut de Mathématiques de Marseille (I2M), France, May 22, 2017.
  18. Geometry Seminar, ETH Zürich, Swiss, May 3, 2017.
  19. Topology Seminar, EPFL, Lausanne, Swiss, April 27, 2017.
  20. Thursday Colloquium, TIFR, Mumbai, India, April 20, 2017.
  21. IBS--CGP Seminar, Pohang, Korea, April 13, 2017.
  22. Department Colloquium, Sungkyunkwan University, Suwon, Korea, April 6.
  23. Topology--Geometry Seminar, Hiroshima University, Japan, March 16, 2017.
  24. Topology Seminar, Osaka University, Japan, March 13, 2017.

For general public

  • Talk concert (for general public), Gwachun National Science Museum, Korea, Aug 19, 2017.
  • Dream Lecture (for general public), Korea Foundation for Advanced Studies, Seoul, Korea, July 15, 2017.

2016

  1. SNU Topology Winter School, December 16,, 2016.
  2. Virginia Topology Conference, University of Virginia, November 18, 2016.
  3. Geometry and Topology Seminar, Seoul National University, November 16, 2016.
  4. Topology Seminar, Sungkyunkwan University, November 15, 2016.
  5. Invited Talk, Korean Mathematical Society Annual Fall Conference, October 22, 2016.
  6. 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, 2017.
  7. Geometric Topology Fair 2016, KAIST, Daejeon, July 7, 2016.
  8. GAGTA (Geometric and Asymptotic Group Theory and Applications) 2016, Stevens Institute of Technology, June 17, 2016.
  9. IBS--CGP seminar, IBS--CGP, Pohang, Korea, April 21, 2016.
  10. Mathematics seminar, Konkuk University, Seoul, Korea, March 25, 2016.
  11. Invited lecture, Korea Institute for Advanced Study (KIAS), Korea, Mar 2, 2016.
  12. Group actions seminar, Yale University, Feb 22, 2016.
  13. Geometry and topology seminar, Univ. of Massachusetts at Amherst, Feb 19, 2016.
  14. Geometric group theory seminar, Tufts University, Feb 18, 2016.
  15. Teichmüller theory and low-dimensional topology, Tsinghua Sanya International Mathematics Forum (TSIMF), China, Jan 11 - 15, 2016. script

2015

  1. East Asian Conference on Algebraic Topology 6 (EACAT-6), Daejeon, November 30 - Dec 4, 2015.
  2. 2015 International Workshop on Mathematical Sciences in Dalian, China, Oct 30 - Nov 1, 2015.
  3. Department Colloquium, Ewha Women's University, Oct 15, 2015.
  4. University of Rennes, France, October 1, 2015.
  5. IBS--CGP Mathematics Festival for Undergraduates, Aug 17 - 21, 2015. script
  6. Dubrovnik VIII - Geometric Topology, Geometric Group Theory and Dynamical Systems, Croatia, June 22 - 26, 2015.
  7. Statistics seminar, Seoul National University, Korea, June 4, 2015.
  8. Geometry & Topology seminar, Postech, Korea, April 22, 2015.
  9. Geometric Group Theory on Gulf Coast (G^3), San Padres Island, USA, March 26 - 29, 2015. script
  10. KIAS Algebra Seminar, KIAS, January 5, 2015.

2014

  1. Group Action Forum, Tsinghua Sanya International Mathematics Forum, China, December 15 -- 19, 2014.
  2. KIAS/CMC Colloquium, KIAS, December 2, 2014.
  3. Department Colloquium, Chiang Mai University, October 28, 2014.
  4. the 7th Mathematical Society of Japan -- Seasonal Institute, Hyperbolic Geometry and Geometric Group Theory (ICM Satellite), Tokyo University, Japan, July 30 - August 5, 2014. script
  5. Discrete Groups and Geometric Structures with Applications V, KU Leuven, Belgium, June 2 - 6, 2014.
  6. Branched Coverings, Degenerations, and Related Topics 2014, Hiroshima University, Japan, March 7, 2014.
  7. Groups and Geometry in the South East, Mathematics Institute, Warwick University, United Kingdom, February 21, 2014.
  8. Complex Analysis and Topology of Discrete Groups and Hyperbolic Spaces, Research Institute for Mathematical Sciences, Kyoto University, Japan, January 24, 2014.

2013

  1. 5th East Asian Conference of Algebraic Topology (EACAT 5), Chinese Academy of Sciences, Beijing, China, December 3, 2013.
  2. Wasatch Topology Conference, the University of Utah, USA, November 16, 2013.
  3. Topology Seminar, University of Texas at Austin, November 11, 2013.
  4. Geometry and Topology Seminar, City University of New York, November 5, 2013.
  5. Discovery-oriented class in calculus, Inha University Pedagogy Workshop, October 28, 2013. script
  6. Korean Mathematical Society Annual Meeting, University of Seoul, Korea, October 25, 2013.
  7. Geometry and Topology Seminar, Brown University, October 9, 2013.
  8. Topology/Geometry Seminar, Yale University, October 8, 2013.
  9. New York Applied Algebra Colloquium, City University of New York, 27 September, 2013.
  10. Geometric and Analytic Group Theory, Ventotene Island, Italy, September 9-14, 2013.
  11. Geometric Structures on Low-Dimensional Manifolds, Korea Institute for Advanced Study, Korea, May 24, 2013.
  12. Discrete Math Seminar, KAIST, April 19, 2013.
  13. Hot Topics: Surface subgroups and cube complexes, Mathematical Sciences Research Institute, USA, March 19, 2013.
  14. Topology and Geometry Seminar, National University of Singapore, February 13, 2013.
  15. Geometric Group Theory and Topology Seminar, Tufts University, January 29, 2013.
  16. Topology/Geometry Seminar, Yale University, January 22, 2013.

2012

  1. Manhattan Algebra Day, Stevens Institute, USA, December 7, 2012.
  2. Topology Seminar, Osaka University, December 4 2012.
  3. Friday Workshop on Geometry of Artin Groups, KIAS, November 23, 2012.
  4. Topology Seminar, Hanyang University, October 19 and October 26, 2012.
  5. Department Colloquium, Sogang University, October 18 2012.
  6. MSJ-KMS Joint Meeting, Kyushu University, Japan, September 17, 2012. script
  7. Topology Seminar, KAIST, September 5 2012.
  8. The 10th KAIST Geometric Topology Fair, KAIST, Daejeon, Korea, August 16, 2012.
  9. Geometric and Asymptotic Group Theory with Applications (GAGTA-6), University of Duesseldorf, July 30, 2012.
  10. Geometric Group Theory - Kyoto 2012, Kyoto University, Japan, June 7, 2012.
  11. Department Colloquium, Ulsan University, April 12 2012.
  12. 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
  13. Geometry and Topology Seminar, SUNY Buffalo, January 25, 2012.
  14. AMS-MAA Joint Meeting, Special session on hyperbolicity in manifolds and groups, Boston, January 4, 2012.

2011

  1. Department Colloquium, Konkuk University, Seoul, Korea, November 17, 2011.
  2. Department Colloquium, Hanyang University, Seoul, Korea, November 4, 2011.
  3. Department Colloquium, Yonsei University, Seoul, Korea, October 13, 2011.
  4. Department Colloquium, Seoul National University, Seoul, Korea, September 29, 2011.
  5. The 4th Topology Workshop, Chonbuk National University, Jeonju, Korea, August 23 - 24, 2011.
  6. The 9th KAIST Geometric Topology Fair, KAIST, Daejeon, Korea, August 9, 2011.
  7. Geometric and Asymptotic Group Theory with Applications (GAGTA--5), Universitat Politecnica de Catalunya, Barcelona, Spain, July 12, 2011.
  8. Dubrovnik VII - Geometric Topology, Inter-University Centre and University of Zagreb, Dubrovnik, Croatia, July 2, 2011.
  9. Geometry/Topology Seminar, University of Chicago, April 12, 2011.
  10. Topology/Geometry Seminar, Yale University, April 5, 2011.
  11. Spring Topology and Dynamics Conference, University of Texas at Tyler, U.S.A., March 18, 2011.
  12. AMS Southeastern Section Meeting, Special Session on Geometric Group Theory, Georgia Southern University, U.S.A., March 13, 2011.
  13. Topology and Geometric Group Theory Seminar, Cornell University, March 8, 2011.
  14. Bernstein Seminar, Cornell University, March 8, 2011.
  15. AMS-MAA Joint Meeting, Special session on groups, geometry and applications, New Orleans, January 7, 2011.

--2010

  1. Topology Seminar, KAIST, Korea, December 23, 2010.
  2. Geometry and Topology Seminar, SUNY Buffalo, November 19, 2010.
  3. Topology Seminar, University of Texas at Austin, November 8, 2010.
  4. Geometry and Topology Seminar, Caltech, October 22, 2010.
  5. Approaches to Group Theory, Using Algebraic, Analytic, and Geometric Tools in the Study of Groups, Cornell University, U.S.A., October 10, 2010.
  6. Topology Seminar, Brandeis University, September 21 2010.
  7. Geometric Group Theory and Topology Seminar, Tufts University, September 14, 2010.
  8. KAIST Topology Workshop, Daejeon, Korea, August 4, 2010.
  9. KAIST--POSTECH--SNU YB Workshop, Jeonju, Korea, July 3, 2010.
  10. Topology Seminar, University of California at Santa Barbara, May 18, 2010.
  11. AMS Special Session on Geometric Group Theory, University of New Mexico, U.S.A., April 18 2010.
  12. Geometric Group Theory Seminar, Tufts University, January 19, 2010.
  13. BK21 Seminar, KAIST, January 26 2010.
  14. Joint Topology and Discrete Math Seminar, KAIST, December 28, 2009.
  15. Topology Seminar, Konkuk University, December 22, 2009.
  16. 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.
  17. Topology/Geometry Seminar, Yale University, October 27, 2009.
  18. Topology Seminar, The University of Texas at Austin, August 31, 2009.
  19. International Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory, the University of Nebraska-Lincoln, U.S.A., May 20, 2009.
  20. AMS Special Session on Recent Progress in Geometric Group Theory, San Francisco State University, April 25, 2009.
  21. Topology Seminar, The University of Texas at Austin, April 13, 2009.
  22. Groups and Dynamics Seminar, Texas A&M University, March 25, 2009.
  23. Topology Seminar, The University of Texas at Austin, October 27, 2008. script
  24. Groups and Infinite Graphs, Erwin Schroedinger International Institute, Austria, August 26, 2008.
  25. Topology Seminar, Seoul National University, Korea, June 2, 2008.
  26. Topology Seminar, The University of Texas at Austin, January 28, 2008. script
  27. Joint Postdoc Seminar, Mathematics Sciences Research Institute, October 19 2007.
  28. Group Actions Seminar, Yale University, October 16, 2006.
  29. Student Seminar (exposition), Yale University, May 1, 2004. script

Public lectures

2017 March 20, 2017 (Young-rak High School), July 15, 2017 (KFAS building).
2016 July 23, July 30 (KFAS building), Seoul High School, October 14.
2015 Kyungshin High School - May 8. Seocho High School - May 29. Seo-oon Middle School - Sep 4. Chil-won High School - Oct 16.
2014 Banpo High School - September 13, 2014. KFAS - December 20, 2014.
  • 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.
  • SNU College of Natural Sciences Public Lecture, Seoul National University, Korea, February 9, 2017.
  • Saturday Public Science Lecture, Seoul National University, Oct 24, 2015.
  • KFAS Dream Lecture (public lecture), KFAS, , 2016.
  • Saturday Public Science Lectures, Seoul National University, March 26, 2016.