Research (Sang-hyun Kim)
Publications
Most papers by Sang-hyun Kim can be downloaded at http://arxiv.org/a/kim_s_3.
Published / to appear
18. (With Thomas Koberda and Mahan Mj), Rotation spectra and exotic group actions on the circle, Springer Lecture Notes in Mathematics, accepted.
- 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.
17. (With 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 C^{1+bv} diffeomorphism group of a compact one-manifold. As a consequence, we have a complete classification of RAAGs that embed into Diff^{r}(S^{1}) for each 0 ≤ r ≤ ω. (The cases r ≤ 1 and r = ω were previously known)
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 C^{1+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 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.
12. (With 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.
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(S^{2}) by a quasi-isometry with word-- or L^{p}--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 S^{2} 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 {G_{i}}, we study the kernel K of the map G -> ∏_{i} G_{i}. We show K embeds into some RAAG. When each G_{i} 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
2. (With Thomas Koberda) Non-freeness of two-generated parabolic groups (with Thomas Koberda)
- 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
1. (With Thomas Koberda) Diffeomorphism groups of critical regularity
- We prove that for each real numbers a ≥ 1, there exists a finitely generated subgroup G_{a} of Diff^{a}(S^{1}) with the property that G_{a} admits no injective homomorphisms into Diff^{b}(S^{1}) for all b > a. We also prove that there exists another fg group H_{a} that embeds into Diff^{b}(S^{1}) for all b < a, but not into Diff^{a}(S^{1}). One can further require the same properties are inherited to all finite index subgroups and to the commutator groups of G_{a} and of H_{a}. The commutator groups will be simple.
Conference proceedings / surveys / other writings
3. Surface subgroups of word-hyperbolic groups, Handbook of group actions. Vol. III, 89-102, Adv. Lect. Math. (ALM), 40, Higher Education Press and International Press, Beijing-Boston (to appear).
- We survey known results on Gromov's question regarding surface subgroups of word-hyperbolic groups.
2. (With Thomas Koberda), RAAGs in Diffeos, Advanced Studies in Pure Mathematics: Volume 73, 215-224.
- We give an exposition on embeddability results related to RAAGs (right-angled Artin groups) and various automorphism groups of manifolds.
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.
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.
2020
2019
- Combinatorial and algebraic aspects of geometric structures – Workshop in Thailand, with the cooperation of Luxembourg, Singapore, and Thailand, Chiang Mai, Thailand, July 18 - 19, 22 - 26, 2019 (scheduled).
- Ordered Groups and Rigidity in Dynamics and Topology, Oaxaca, Mexico, June 16 - 21, 2019 (scheduled).
- Non-positive curvature, Warsaw, Poland, May 20 - 24, 2019 (scheduled).
- Special Sessions on Mapping Class Groups, University of Hawaii at Manoa, Honolulu, US, March 22 - 24, 2019 (scheduled).
- East Asian Conference of Geometric Topology, Beijing, China, January 19 - 23, 2019.
- Suzhou 2019 Workshop on Geometry Topology, Soochow University, Suzhou, China, January 17–20, 2019.
2018
- 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.
- 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.
- 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, 2018.
2017
- 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: JCDCG^{3}, Tokyo University of Science (Aug 29 - Sep 1), Tokyo, Japan, August 29, 2017.
- Japanese Topology Symposium, Tokai University, Tokyo, Japan, August 21 -- 24, 2017, 2017.
- Invited talk, Korea Institute for Advanced Study (KIAS), Korea, Aug 7, 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.
- Topology 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.
- Topology--Geometry Seminar, Hiroshima University, Japan, March 16, 2017.
- Topology Seminar, Osaka University, Japan, March 13, 2017.
- SNU Geometry and Topology Mini-Workshop, Seoul National University, Korea, February 17, 2017.
2016
- 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.
- 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.
- 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.
- 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. script
2015
- 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.
- Department Colloquium, Ewha Women's University, Oct 15, 2015.
- University of Rennes, France, October 1, 2015.
- IBS--CGP Mathematics Festival for Undergraduates, Aug 17 - 21, 2015. script
- Dubrovnik VIII - Geometric Topology, Geometric Group Theory and Dynamical Systems, Croatia, June 22 - 26, 2015.
- Statistics seminar, Seoul National University, Korea, June 4, 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. script
- KIAS Algebra Seminar, KIAS, January 5, 2015.
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.
- 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
- Discrete Groups and Geometric Structures with Applications V, KU Leuven, Belgium, June 2 - 6, 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.
2013
- 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. script
- 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, 2013.
- 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, 2013.
- Geometric Group Theory and Topology Seminar, Tufts University, January 29, 2013.
- Topology/Geometry Seminar, Yale University, January 22, 2013.
2012
- 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. script
- 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. script
- 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.
2011
- 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, 2011.
- 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.
--2010
- 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, 2010.
- 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. script
- 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. script
- 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. script
Public lectures
Seoul National University
- Young Mathematicians' Camp, National Institute for Mathematical Sciences, Daejeon, February 22, 2017.
- SNU College of Natural Sciences Public Lecture, Seoul National University, Korea, February 9, 2017. video
- Science Camp, College of Natural Sciences, Seoul National University, (1) August 3, 2016 (2) August 9, 2018. [1]
- Saturday Public Science Lectures, College of Natural Sciences, Seoul National University, March 26, 2016.
- Saturday Public Science Lecture, College of Natural Sciences, Seoul National University, Oct 24, 2015.
Dream Lecture Series
by Korea Foundation for Advanced Studies
- 2018 May 12 (KFAS building), May 14 (Hanyoung Foreign Language High School)
- 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 Sep 13, 2014 (Banpo High School). Dec 20, 2014, KFAS.
Others
- Talk concert (for general public), Gwachun National Science Museum, Korea, Aug 19, 2017.
Videos
- 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)