Byunghee An

Byung Hee An

Byung Hee An is an associate professor at Department of Mathematics Education of Kyungpook National University.

Education and Employment

Mar. 1997 – Feb. 2001
B.S. in Mathematics, KAIST
Mar. 2001 – Feb. 2003
M.S. in Mathematics, KAIST
Thesis: Cryptanalysis on braid cryptosystem via the Krammer representation
Advisor: Ki Hyoung Ko
Mar. 2003 – Feb. 2010
Ph.D. in Mathematics, KAIST
Thesis: A family of representations of braid groups on surfaces
Advisor: Ki Hyoung Ko
Feb. 2010 – Aug. 2012
Postdoc, PMI, POSTECH
Sep. 2012 – Feb. 2013
Postdoc, KIAS
Mar. 2013 – Feb. 2020
Tenure-track Research fellow, IBS-CGP
Mar. 2020 – Mar. 2024
Assistant Professor, Department of Mathematics Education, Kyungpook National University
Feb. 2022 – Aug. 2022
Deputy Chair of the Department, Department of Mathematics Education, Kyungpook National University
Sep. 2022 – Aug. 2023
Vice Dean of the College, Teachers College, Kyungpook National University
Sep. 2023 – Present
(Deputy) Chair of the Department, Department of Mathematics Education, Kyungpook National University
Apr. 2024 – Present
Associate Professor, Department of Mathematics Education, Kyungpook National University

Research

Research Interests
  • classical knot theory, singular knots and spatial graphs, Legendrian knots and graphs, modern invariants of Legendrian graphs and tangles,
  • group theoretic problems of braid groups, braid groups on surfaces and complexes, configuration space of graphs, algebra and coalgebra structures on configuration spaces.
Research subjects currently I am working on
  • Modern invariants of Legendrian graphs and tangles
    • joint with Youngjin Bae(INU), Tamás Kálmán(TIT), Seonhwa Kim(KIAS), Eunjeong Lee(IBS-CGP), and Tao Su(ENS)
    • Papers: published (or accepted), under review, and in preparation
  • Homotopy invariants of configuration spaces of graphs
    • joint with Gabriel C. Drummond-Cole(Facebook), Ben Knudsen(Northeastern University), and Tomasz Maciążek(University of Bristol),
    • Papers: published (or accepted), and in preparation
  • and others.

Papers

peer-reviewed publications
  1. The automorphism groups of Artin groups of edge-separated CLTTF graphs, Journal of the Korean Mathematical Society, 60(6), 1171–1213 (2023). arXiv DOI Abstract
    (with Youngjin Cho(KNU))
    This work is a continuation of Crisp's work on automorphism groups of CLTTF Artin groups, where the defining graph of a CLTTF Artin group is connected, large-type, and triangle-free. More precisely, we provide an explicit presentation of the automorphism group of an edge-separated CLTTF Artin group whose defining graph has no separating vertices.
  2. Augmentations are sheaves for Legendrian graphs, Journal of Symplectic Geometry, 20(2), 250–416 (2022). arXiv DOI Abstract
    (with Youngjin Bae(KIAS) and Tao Su(ENS))
    In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legendrian isotopy invariants: the augmentation category, a unital $A_\infty$-category, which lifts the set of augmentations of the associated Chekanov-Eliashberg DGA, and a DG category of constructible sheaves on the front plane, with micro-support at contact infinity controlled by the (bordered) Legendrian graph. In other words, generalizing [21], we prove "augmentations are sheaves" in the singular case.
  3. Asymptotic homology of graph braid groups, Geometry & Topology, 26(4), 1745–1771 (2022). arXiv DOI Abstract
    (with Gabriel C. Drummond-Cole and Ben Knudsen(Northeastern University))
    We give explicit formulas for the asymptotic Betti numbers of the unordered configuration spaces of an arbitrary finite graph over an arbitrary field.
  4. Augmentations and ruling polynomials for Legendrian graphs, Algebraic & Geometric Topology, 22(5), 2079–2085 (2022). arXiv DOI Abstract
    (with Youngjin Bae(INU) and Tao Su(ENS))
    In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two Legendrian isotopy invariants: augmentation number via point-counting over a finite field, for the augmentation variety of the associated Chekanov-Eliashberg differential graded algebra, and ruling polynomial via combinatorics of the decompositions of the associated front projection.
  5. Ruling invariants for Legendrian graphs, Journal of Symplectic Geometry, 20(1), 49–98 (2022). DOI arXiv Abstract
    (with Youngjin Bae(INU) and Tamás Kálmán(TIT))
    We define ruling invariants for even-valence Legendrian graphs in standard contact three-space. We prove that rulings exist if and only if the DGA of the graph, introduced by the first two authors, has an augmentation. We set up the usual ruling polynomials for various notions of gradedness and prove that if the graph is four-valent, then the ungraded ruling polynomial appears in Kauffman-Vogel's graph version of the Kauffman polynomial. Our ruling invariants are compatible with certain vertex-identifying operations as well as vertical cuts and gluings of front diagrams. We also show that Leverson's definition of a ruling of a Legendrian link in a connected sum of $S^1\times S^2$'s can be seen as a special case of ours.
  6. On folded cluster patterns of affine type, Pacific Journal of Mathematics, 381(2), 401–431 (2022). DOI arXiv Abstract
    (with Eunjeong Lee(CBNU))
    A cluster algebra is a commutative algebra whose structure is decided by a skew-symmetrizable matrix or a quiver. When a skew-symmetrizable matrix is invariant under an action of a finite group and this action is admissible, the folded cluster algebra is obtained from the original one. Any cluster algebra of non-simply-laced affine type can be obtained by folding a cluster algebra of simply-laced affine type with a specific $G$-action. In this paper, we study the combinatorial properties of quivers in the cluster algebra of affine type. We prove that for any quiver of simply-laced affine type, $G$-invariance and $G$-admissibility are equivalent. This leads us to prove that the set of $G$-invariant seeds forms the folded cluster pattern.
  7. On the second homology of planar graph braid groups, Journal of Topology, 15(2), 666–691 (2022). DOI arXiv Abstract
    (with Ben Knudsen(Northeastern University))
    We show that the second homology of the configuration spaces of a planar graph is generated under the operations of embedding, disjoint union, and edge stabilization by three atomic graphs: the cycle graph with one edge, the star graph with three edges, and the theta graph with four edges. We give an example of a non-planar graph for which this statement is false.
  8. Geometric presentations of graph braid groups for Particles on a Graph, Communications in Mathematical Physics, 384(2), 1109–1140 (2021). DOI arXiv Abstract
    (with Tomasz Maciążek(University of Bristol))
    We study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators consists of exchanges of pairs of particles on junctions of the graph and of certain circular moves where one particle travels around a simple cycle of the graph. We point out that so defined generators often do not satisfy the braiding relation known from 2D physics. We accomplish a full description of relations between the generators for star graphs where we derive certain quasi-braiding relations. We also describe how graph braid groups depend on the (graph-theoretic) connectivity of the graph. This is done in terms of quotients of graph braid groups where one-particle moves are put to identity. In particular, we show that for $3$-connected planar graphs such a quotient reconstructs the well-known planar braid group. For $2$-connected graphs this approach leads to generalisations of the Yang-Baxter equation. Our results are of particular relevance for the study of non-abelian anyons on networks showing new possibilities for non-abelian quantum statistics on graphs.
  9. Universal properties of anyon braiding on one-dimensional wire networks, Physical Review B, 102(20), Issue 20, 201407(R) (2020). DOI arXiv Abstract
    (with Tomasz Maciążek(University of Bristol))
    We demonsrtrate that anyons on wire networks have fundamentally different braiding properties than anyons in 2D. Our analysis reveals an unexpectedly wide variety of possible non-abelian braiding behaviours on networks. The character of braiding depends on the topological invariant called the connectedness of the network. As one of our most striking consequences, particles on modular networks can change their statistical properties when moving between different modules. However, sufficiently highly connected networks already reproduce braiding properties of 2D systems. Our analysis is fully topological and independent on the physical model of anyons.
  10. A Chekanov-Eliashberg algebra for Legendrian graphs, Journal of Topology, 13(2), 777–869 (2020). DOI arXiv Abstract
    (with Youngjin Bae(KIAS))
    We define a differential graded algebra for Legendrian graphs and tangles in the standard contact Euclidean three space. This invariant is defined combinatorially by using ideas from Legendrian contact homology. The construction is distinguished from other versions of Legendrian contact algebra by the vertices of Legendrian graphs. A set of countably many generators and a generalized notion of equivalence are introduced for invariance. We show a van Kampen type theorem for the differential graded algebras under the tangle replacement. Our construction recovers many known algebraic constructions of Legendrian links via suitable operations at the vertices.
  11. Edge stabilization in the homology of graph braid groups, Geometry & Topology, 24(1), 421–469 (2020). DOI arXiv Abstract
    (with Gabriel C. Drummond-Cole(IBS-CGP) and Ben Knudsen(Harvard University))
    We introduce a novel type of stabilization map on the configuration spaces of a graph, which increases the number of particles occupying an edge. There is an induced action on homology by the polynomial ring generated by the set of edges, and we show that this homology module is finitely generated. An analogue of classical homological and representation stability for manifolds, this result implies eventual polynomial growth of Betti numbers. We calculate the exact degree of this polynomial, in particular verifying an upper bound conjectured by Ramos. Because the action arises from a family of continuous maps, it lifts to an action at the level of singular chains, which contains strictly more information than the homology level action. We show that the resulting differential graded module is almost never formal over the ring of edges.
  12. Subdivisional spaces and graph braid groups, Doc. Math., 24, 1513–1583 (2019). DOI arXiv Abstract
    (with Gabriel C. Drummond-Cole(IBS-CGP) and Ben Knudsen(Harvard University))
    We study the problem of computing the homology of the configuration spaces of a finite cell complex $X$. We proceed by viewing $X$, together with its subdivisions, as a subdivisional space--a kind of diagram object in a category of cell complexes. After developing a version of Morse theory for subdivisional spaces, we decompose $X$ and show that the homology of the configuration spaces of $X$ is computed by the derived tensor product of the Morse complexes of the pieces of the decomposition, an analogue of the monoidal excision property of factorization homology. Applying this theory to the configuration spaces of a graph, we recover a cellular chain model due to Świątkowski. Our method of deriving this model enhances it with various convenient functorialities, exact sequences, and module structures, which we exploit in numerous computations, old and new.
  13. On the Chern numbers for pseudo-free circle actions, J. Symplectic Geom., 17(1), 1–40 (2019). DOI arXiv Abstract
    (with Yunhyung Cho(SKKU))
    Let $(M,\psi)$ be a $(2n+1)$-dimensional oriented closed manifold with a pseudo-free $S^1$-action $\psi : S^1 \times M \rightarrow M$. We first define a \textit{local data} $\mathcal{L}(M,\psi)$ of the action $\psi$ which consists of pairs $(C, (p(C) ; \overrightarrow{q}(C)))$ where $C$ is an exceptional orbit, $p(C)$ is the order of isotropy subgroup of $C$, and $\overrightarrow{q}(C) \in (\mathbb{Z}_{p(C)}^{\times})^n$ is a vector whose entries are the weights of the slice representation of $C$. In this paper, we give an explicit formula of the Chern number $\langle c_1(E)^n, [M/S^1] \rangle$ modulo $\mathbb{Z}$ in terms of the local data, where $E = M \times_{S^1} \mathbb{C}$ is the associated complex line orbibundle over $M/S^1$. Also, we illustrate several applications to various problems arising in equivariant symplectic topology.
  14. Legendrian singular links and singular connected sums, J. Symplectic Geom., 16(4), 885–930 (2018). DOI arXiv Abstract
    (with Youngjin Bae(RIMS) and Seonhwa Kim(IBS-CGP))
    We study Legendrian singular links up to contact isotopy. Using a special property of the singular points, we define the singular connected sum of Legendrian singular links. This concept is a generalization of the connected sum and can be interpreted as a tangle replacement, which provides a way to classify Legendrian singular links. Moreover, we investigate several phenomena only occur in the Legendrian setup.
  15. Grid diagrams for singular links, J. Knot Theory Ramification, 27(4), 1850023, 43pp (2018). DOI arXiv Abstract
    (with Hwa Jeong Lee(DGIST))
    In this paper, we define the set of singular grid diagrams $\mathcal{SG}$ which provides a unified description for singular links, singular Legendrian links, singular transverse links, and singular braids. We also classify the complete set of all equivalence relations on $\mathcal{SG}$ which induce the bijection onto each singular object. This is an extension of the known result of Ng–Thurston [Grid diagrams, braids, and contact geometry, in Proc. Gökova Geometry-Topology Conf. 2008, Gökova Geometry/Topology Conference (GGT), Gökova, 2009, pp. 120–136] for nonsingular links and braids.
  16. On the $f$-vectors of Gelfand-Cetlin polytopes, European J. Combin., 67, 61–77 (2018). DOI arXiv Abstract
    (with Yunhyung Cho(SKKU) and Jang Soo Kim(SKKU))
    A Gelfand–Cetlin polytope is a convex polytope obtained as an image of certain completely integrable system on a partial flag variety. In this paper, we give an equivalent description of the face structure of a GC-polytope in terms of so called the face structure of a ladder diagram. Using our description, we obtain a partial differential equation whose solution is the exponential generating function of $f$-vectors of GC-polytopes. This solves the open problem (2) posed by Gusev et al. (2013).
  17. On the structure of braid groups on complexes, Topology Appl., 226, 86–119 (2017). DOI arXiv Abstract
    (with Hyowon Park(PMI))
    We consider the braid group $\mathbf{B}_n(X)$ on a finite simplicial complex $X$, which is a generalization of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions for $X$ and their effects on the braid groups. As applications, we give complete criteria for both the surface embeddability and planarity for $X$, which are the torsion-freeness of the braid group $\mathbf{B}_n(X)$ and its abelianization $H_1(\mathbf{B}_n(X))$, respectively.
  18. A criterion for the Legendrian simplicity of the connected sum, Topology Appl., 204, 175–184 (2016). DOI arXiv Abstract
    In this paper, we provide the necessary and sufficient conditions for the connected sum of knots in $S^3$ to be Legendrian simple.
  19. Automorphisms of braid groups on orientable surfaces, J. Knot Theory Ramification, 25(5), 1650022, 32pp (2016). DOI arXiv Abstract
    In this paper we compute the automorphism groups $\operatorname{Aut}(\mathbf{P}_n(\Sigma))$ and $\operatorname{Aut}(\mathbf{B}_n(\Sigma))$ of braid groups $\mathbf{P}_n(\Sigma)$ and $\mathbf{B}_n(\Sigma)$ on every orientable surface $\Sigma$, which are isomorphic to group extensions of the extended mapping class group $\mathcal{M}^*_n(\Sigma)$ by the transvection subgroup except for a few cases. We also prove that $\mathbf{P}_n(\Sigma)$ is always a characteristic subgroup of $\mathbf{B}_n(\Sigma)$ unless $\Sigma$ is a twice-punctured sphere and $n=2$.
  20. A family of pseudo-Anosov braids with large conjugacy invariant sets, J. Knot Theory Ramification, 22(6), 1350025, 20pp (2013). DOI arXiv Abstract
    (with Ki Hyoung Ko(KAIST))
    We show that there is a family of pseudo-Anosov braids independently parametrized by the braid index and the (canonical) length whose smallest conjugacy invariant sets grow exponentially in the braid index and linearly in the length.
  21. A family of representations of braid groups on surfaces, Pacific J. Math., 247(2), 257–282 (2010). DOI arXiv Abstract
    (with Ki Hyoung Ko(KAIST))
    We propose a family of homological representations of the braid groups on surfaces. This family extends linear representations of the braid groups on a disc, such as the Burau representation and the Lawrence-Krammer-Bigelow representation.
others
  1. A family of representations of braid groups on surfaces, Ph.D. Thesis, KAIST (2010). Thesis
  2. Security Consideration in Ubiquitous Environments of the Project "iWearCom", Proceedings of Next Generation PC 2005 International Conference, Korea Institute of Next Generation PC, 79–85 (2005). Proceeding
    (with Ki Hyoung Ko(KAIST) et al)
  3. In search of representations of braid group on surfaces, Proceedings of 2nd East Asian School of knots and related topics in geometric topology, 15–20 (2005).
  4. Cryptanalysis on braid cryptosystem via the Krammer representation, M.S. Thesis, KAIST (2003). Thesis
preprints and papers under review
  1. Lagrangian fillings for Legendrian links of finite or affine Dynkin type, submitted, arXiv:2201.00208. arXiv Abstract
    (with Youngjin Bae(INU) and Eunjeong Lee(IBS-CGP))

    This is a unified version of .

    We prove that there are at least as many exact embedded Lagrangian fillings as seeds for Legendrian links of finite type $\mathsf{ADE}$ or affine type $\widetilde{\mathsf{D}}\widetilde{\mathsf{E}}$. We also provide as many Lagrangian fillings with rotational symmetry as seeds of type $\mathsf{B}$, $\mathsf{G}_2$, $\widetilde{\mathsf{G}}_2$, $\widetilde{\mathsf{B}}$, or $\widetilde{\mathsf{C}}_2$, and with conjugation symmetry as seeds of type $\mathsf{F}_4$, $\mathsf{C}$, $\mathsf{E}^{(2)}_6$, $\widetilde{\mathsf{F}}_4$, or $\mathsf{A}^{(2)}_5$. These families are the first known Legendrian links with (infinitely many) exact Lagrangian fillings (with symmetry) that exhaust all seeds in the corresponding cluster structures beyond type $\mathsf{AD}$. Furthermore, we show that the $N$-graph realization of (twice of) Coxeter mutation of type $\widetilde{\mathsf{D}}\widetilde{\mathsf{E}}$ corresponds to a Legendrian loop of the corresponding Legendrian links. Especially, the loop of type $\widetilde{\mathsf{D}}$ coincides with the one considered by Casals and Ng.
  2. Lagrangian fillings for Legendrian links of affine type, arXiv:2107.04283. arXiv Abstract
    (with Youngjin Bae(INU) and Eunjeong Lee(IBS-CGP))
    We prove that there are at least as many exact embedded Lagrangian fillings as seeds for Legendrian links of affine type $\tilde{D}\tilde{E}$. We also provide as many Lagrangian fillings with certain symmetries as seeds of type $\tilde{B}_n$, $\tilde{F}_4$, $\tilde{G}_2$, and $E^{(2)}_6$. These families are the first known Legendrian links with infinitely many fillings that exhaust all seeds in the corresponding cluster structures. Furthermore, we show that Legendrian realization of Coxeter mutation of type $D$ corresponds to the Legendrian loop considered by Casals and Ng.
  3. Lagrangian fillings for Legendrian links of finite type, arXiv:2101.01943. arXiv Abstract
    (with Youngjin Bae(INU) and Eunjeong Lee(IBS-CGP))
    We prove that there are at least seeds many exact embedded Lagrangian fillings for Legendrian links of type $\mathsf{ADE}$. We also provide seeds many Lagrangian fillings with certain symmetries for type $\mathbf{BCFG}$. Our main tools are $N$-graphs and the combinatorics of seed patterns of finite type.
papers in preparation
  1. Cup and shuffle products in the cohomology of configuration spaces, in preparation.
  2. Geometry behind the construction of DGA for Legendrian graphs, in preparation.
    (with Youngjin Bae(INU))
  3. Geometro-analytic definition of An-Bae's DGA of Legendrian graphs, in preparation.
    (with Youngjin Bae(INU) and Yong-Geun Oh(IBS-CGP))
  4. Quasi-isometric classification of configuration spaces of trees, in preparation.
    (with Sangrok O(KNU))

Teaching

2023 Fall
  1. Guidance of Geometry 2
  2. Modern Differential Geometry 2
2023 Spring
  1. Modern Differential Geometry 1
  2. Guidance of Geometry 1
  3. Topics in Geometry
  4. Dissertation and Research Ethics : Mathematics Education
2022 Fall
  1. Calculus II
  2. Modern Differential Geometry 2
2022 Spring
  1. Modern Differential Geometry 1
  2. Guidance of Geometry 1
  3. Advanced Discrete Mathematics Education
2021 Fall
  1. Modern Differential Geometry 2
  2. Advanced Topology
  3. Dissertation and Research Ethics : Mathematics Education
2021 Spring
  1. Modern Differential Geometry 1
  2. Guidance of Geometry 1
  3. Dissertation and Research Ethics : Mathematics Education
2020 Fall
  1. Modern Differential Geometry 2
  2. Teaching Logic & Writing : Mathematics
  3. Topics in Geometry
2020 Spring
  1. Calculus I
  2. Modern Differential Geometry 1

Invited and contributed Talks

  1. Legendrian graphs and ruling polynomial I, II, Low Dimensional Topology Seminar 2021, Hanyang University, January 21–22, 2021, online(zoom).
  2. Lagrangian fillings for Legendrian links of finite type, Topology Seminar, Incheon National University, January 19, 2021, online(zoom).
  3. Lagrangian fillings for Legendrian links of finite type, Legendrians, Cluster algebras and Mirror symmetry, January 12, 2021, online(zoom).
  4. Knots and their invariants, Incheon National University Math. Dept. Colloquium, November 23, 2020, Incheon National University, Incheon, Korea.
  5. Configuration spaces of graphs, Workshop on Geometry and Topology around Young-Nam, November 20, 2020, Kyungpook National University, Daegu, Korea.
  6. Configuration spaces of graphs, Topology Seminar in Mathematics Department, October 30, 2020, Kyungpook National University, Daegu, Korea.
  7. A Chekanov-Eliashberg DGA for Legendrian graphs, IBS 8th year review, July 9, 2020, IBS-CGP, Pohang, Korea.
  8. Edge stabilization in graph configuration space I, II, Topology Seminar, February 18–19, 2020, Dongguk University Gyeongju, Gyeongju, Korea.
  9. Generators and growth of homology groups of graph braid groups, Configuration spaces of graphs, February 4, 2020, American Institute of Mathematics, San Jose, United States.
    [More]
  10. Legendrians and constructible sheaves, The 15th KIAS Geometry Winter School, December 29, High-1 Resort, Jeongseon, Korea.
  11. Augmentations are sheaves for Legendrian graphs, Topology Seminar, October 28, Yonsei University, Seoul, Korea.
  12. Augmentations are sheaves for Legendrian graphs, The 2019 KMS Fall meeting, October 26, Hongik University, Seoul, Korea.
  13. Augmentation varieties and cluster algebras for Legendrian $(2,n)$ torus knots, The 4th Mini Workshop on Knot theory, June 8, Dongguk University Gyeongju, Gyeongju, Korea.
  14. Augmentation varieties and cluster algebras for Legendrian $(2,n)$ torus knots, AORC Seminar, June 4, Sungkyunkwan University, Suwon, Korea.
  15. Edge stabilization in the homology of graph braid groups, The 14th East Asian Conference on Geometric Topology, January 21, Peking University, Beijing, China.
  16. Braid groups and configuration spaces of graphs, KIAS Geometry Winter School, December 19–20, 2018, High-1 Resort, Jeongseon, Korea.
  17. An introduction to graph braid groups, UGRP Seminar, DGIST, December 12, 2018, Daegu, Korea.
  18. Braid groups and configuration spaces of graphs, Yonsei Math Colloquium 2018, October 25, 2018, Yonsei University, Seoul, Korea.
  19. Three Lectures on Mathematics of knots and braids, Summer School of Gyeongbuk Center for Gifted Students, August, 2018, Gyeongbuk University, Daegu, Korea.
  20. Edge stabilization in the homology of graph braid groups, Geometric and Asymptotic Group Theory with Applications(GAGTA) 2018, July 17, 2018, KIAS, Seoul, Korea.
  21. Subdivisional spaces and configuration spaces of graphs, Topology Seminar, May 16, 2018, Tokyo Institute of Technology, Tokyo, Japan.
  22. Formality of configuration spaces of graphs, 2018 KMS Spring Meeting, April 21, 2018, Kyung Hee University, Seoul, Korea.
  23. Knot theory and its generalizations in Contact geometry, IBS 5th year Symposium, August 28, 2017, POSCO International Center, Pohang, Korea.
  24. Configuration spaces of graphs, Computational and Algorithmic Topology, Sydney 2017 (CATS2017), University of Sydney, June 27, 2017, Sydney, Australia.
  25. An introduction to braid theory, 2017 Inchon University Math. Dept. Colloquium, Inchon National University, May 8, 2017, Inchon, Korea.
  26. Configuration spaces of graphs, 2017 KMS Spring Meeting, Chosun University, April 29, 2017, Gwangju, Korea.
  27. Configuration spaces of graphs, Topology Seminar, DGIST, April 6, 2017, Daegu, Korea.
  28. An introduction to Braid theory, UGRP Seminar, DGIST, April 5, 2017, Daegu, Korea.
  29. DGA invariant for Legendrian graphs, The 2nd Shinchon Workshop on Algebraic Geometry (SWAG 2), Yonsei University, February 27, 2017, Seoul, Korea.
  30. On the $f$-vectors of Gelfand-Tsetlin polytopes, OCAMI Topology Seminar, Osaka City University, February 20, 2017, Osaka, Japan.
  31. Grid diagrams for singular links, The 12th East Asian School of Knots and Related Topics, University of Tokyo, February 13, 2017, Tokyo, Japan.
  32. DGA invariants for Legendrian spatial graphs, The 2nd Mini workshop on knot theory, IBS-CGP, December 17, 2016, Pohang, Korea.
  33. $f$-vectors for Gelfand-Cetlin polytope, Combinatorics seminar, KIAS, September 8, 2016, Seoul, Korea.
  34. Chekanov-Eliashberg algebra for Legendrian singular links, Low-dimensional topology seminar, Chung-Ang university, August 29 2016, Seoul, Korea.
  35. Chekanov-Eliashberg algebra for Legendrian singular links, Knots in hellas 2016, International Olympic Academy, July 19 2016, Ancient Olympia, Greece.
  36. $f$-vectors for Gelfand-Cetlin polytope, KPPY Combinatorics seminar, Pusan University, April 30, 2016, Busan, Korea.
  37. Chekanov-Eliashberg algebra for Legendrian singular links, Topology Seminar, Hannam University, April 27, 2016, Daejeon, Korea.
  38. Grid diagrams for singular knots, Konkuk University Topology Seminar, March 11, 2016, Seoul, Korea.
  39. On the Chern numbers of pseudo-free circle actions, Seoul National University Topology Seminar, February 12, 2016, Seoul, Korea.
  40. Grid diagrams for singular knots, KAIST Topology Seminar, February 11, 2016, Daejeon, Korea.
  41. On the Chern numbers of pseudo-free circle actions, KIAS Topology Seminar, January 19, KIAS, Korea.
  42. Legendrian singular links and singular connected sums, The 1st Pan Pacific International Conference on Topology and Applications, November 26, 2015, Min Nan Normal University, Zhangzhou, China.
  43. Grid diagrams for singular knots, Knots and Spatial Graphs 2015, November 5--7, 2015, Daejeon, Korea.
  44. Grid diagrams for singular knots, T-Seminar, October 6, 2015, Postech, Korea.
  45. Legendrian singular links and singular connected sums, Korean-French Conference in Mathematics, August 27, 2015, POSTECH, Korea.
  46. Criterion for the Legendrian simplicity of connected sum of knots, 2015 KMS Spring Meeting, April 25, 2015, Busan, Korea.
  47. Legendrian singular links and singular connected sums, KAIST Topology Seminar, March 24, 2015, KAIST, Korea.
  48. Criterion for the Legendrian simplicity of connected sum of knots, The 10th East Asian School of Knots and Related Topics, January 27, 2015, Shanghai, China.
  49. Braid groups on CW complexes, KIAS Seminar, August 20, 2014, KIAS, Korea.
  50. Braid Functor, Low Dimensional Topology and Related Topics, July 26, 2014, KAIST, Korea.
  51. Braid groups on CW complexes, KAIST Math. Seminar, Feb 3--5, 2014, KAIST, Korea.
  52. Braid groups on CW complexes, The 1st IBS Research Conference, November 27--28, 2013, Daejeon, Korea.
  53. Braid groups on CW complexes, Center for Geometry and Physics Seminar, August 1, 2013, IBS-CGP, Korea.
  54. Braid groups on CW complexes, T-Seminar, May 16, 2013, Postech, Korea.
  55. Automorphisms of braid groups on orientable surfaces, The 9th East Asian School of Knots and Related Topics, January 15, 2013, University of Tokyo, Japan.
  56. Automorphisms of surface braid groups, 2012 KMS Fall Meeting, October 4, 2012, DCC, Daejeon, Korea.
  57. On the structure of braid groups on complexes, PMI Workshop, June, 2012, Pusan, Korea.
  58. On the structure of braid groups on complexes, Colloquium of Math. dept., May 18, 2012, Chung-Ang University, Korea.
  59. Geometric automorphisms of braid groups on surfaces, The 8th East Asian School of Knots and Related Topics, January 9, 2012, KAIST, Korea.
  60. On the structure of braid groups on complexes, Colloquium of Math. dept., December 16, 2011, Chonbuk National University, Korea.
  61. Geometric automorphisms of braid groups on surfaces, KAIST Topology seminar, December 13, 2011, KAIST, Korea.
  62. On injectivity of braid functor, 2011 KMS Fall Meeting, October 21, 2011, Kyungpook National University, Daegu, Korea.
  63. When does $\mathbf{B}_n(X)$ determine $X$?, PMI Annual workshop, September 23, 2011, Postech, Korea.
  64. A family of representations of braid groups on surfaces, Invited Talk, August 23, 2011, KIAS, Korea.
  65. Braid groups on finite cubical complexes, The 7th East Asian School of Knots and Related Topics, January 12, 2011, Hiroshima University, Japan.
  66. Braid groups and their representations, T-Seminar, April 07, 2010, Postech, Korea.
  67. Questions on braid groups, POSTECH Math Department / BK21 / PMI Faculty, Researchers, & Graduate Students Workshop, February 22, 2010, Novotel Ambassador Hotel, Busan, Korea.
  68. A family of braids with large conjugacy invariant sets, the Joint Meeting of the KMS and the AMS, December 18, 2009, Ewha Womans university, Korea.
  69. A family of permutation braids whose reduced super summit set grows exponentially, The 5th East Asian School of Knots, Links and Related Topics, January 13, 2009, Gyeongju, Korea.
  70. Representations of braid groups on surfaces, The 3rd East Asian School of Knots, Links and Related Topics, February 8, 2007, Osaka city university, Japan.
  71. In search of representations of braid group on surfaces, The 2nd East Asian School of Knots and Related Topics in geometric topology, August 4, 2005, Dalian university of technology, China.
  72. Attack on BDHP via Krammer representation and linear algebra, The 10th Japan-Korea School of Knots and Links, February 21, 2003, Tokyo university, Japan.
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Other Activities

Honors and Awards
  1. Research Grant(중견연구후속, RS-2023-00208405), Legendrians and Cluster structures, March 2023 – February 2026, KRW 450Million, National Research Foundation, Korea.
  2. Research Grant(삼성미래기술육성사업, SSTF-BA2202-03), Homotopy invariants of configuration spaces, December 2022 – November 2027, KRW 750Million, Samsung Science & Technology Foundation, Korea.
  3. Research Grant(중견연구, 2020R1A2C1A01003201), Legendrian, Fukaya Category and Mirror Symmetry, March 2020 – February 2023, KRW 450Million, National Research Foundation, Korea.
  4. 2019, Best Research of the year, January 2, 2020, Institute for Basic Science.
Conferences (co)organized
  1. Organizer, The 4th Workshop for Young Symplectic Geometers, August 16–18, 2022, Incheon National University, Incheon.
  2. Organizer, The 3rd Workshop for Young Symplectic Geometers, February 18–20, 2022, Yonsei University, Seoul.
  3. Organizer, The 2nd Workshop for Young Symplectic Geometers, August 20–22, 2021, Ramada Plaza Hotel, Jeju.
  4. Organizer, Workshop for Young Symplectic Geometers, June 18–20, 2021, Kyungpook National University, Daegu.
  5. Organizer, Legendrians, Cluster algebras, and Mirror symmetry, January 4–8, 11–15, 2021, Online.
  6. Organizer, Workshop on Geomery and Topology around Young-Nam, November 19–21, 2020, Kyungpook National University, Daegu. Proceeding
  7. Organizer, The 5th Mini Workshop on knot theory, July 19–23, 2020, Maison Glad Hotel Jeju, Jeju. Proceeding
  8. Organizer, The 4th Mini Workshop on knot theory, June 7–8, 2019, Dongguk University Gyeongju.
  9. Organizer, 2017 Pohang Mathematics Workshop, December 7–10, 2017, IBS-CGP.
  10. Organizer, The 3rd Mini Workshop on knot theory, June 16–17, 2017, Korea University.
  11. Organizer, The 2nd Mini Workshop on knot theory, December 16–17, 2016, IBS-CGP.
  12. Organizer, Mini Workshop on knot theory, August 19–20, 2016, IBS-CGP.
  13. Organizer, Pohang Mathematics Workshop, November 15–17, IBS-CGP.
  14. Organizer, Friday Workshop of Geometry of Artin Groups, Fall 2012, KIAS/KAIST.
  15. Local Organizer, The 8th East Asian School of Knots and Related Topics, January 9–12, 2012, KAIST.
IT related
  1. Engineer Information Processing, National Qualification by HRD Korea, August 2002.
  2. Server Administrator, Knot Theory and Cryptography Research Group, http://knot.kaist.ac.kr, September 2001– February 2010, KAIST.
  3. IT Administrator, IBS Center for Geometry and Physics, March 2013–February 2020.