Byunghee An

Byung Hee An

Byung Hee An is a tenure-track research fellow, and the IT system administrator of Institute for Basic Science, Center for Geometry and Physics since 2013.

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 – Present
Tenure-track Research fellow, IBS-CGP

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(RIMS), Tamás Kálmán(TIT), Seonhwa Kim(IBS-CGP)
    • Papers: in press, under revision and in preparation
  • Homotopy invariants of configuration spaces of graphs
    • joint with Gabriel C. Drummond-Cole(IBS-CGP) and Ben Knudsen(Harvard University)
    • Papers: under review, in preparation
  • and others.

Papers

peer-reviewed publications
  1. On the Chern numbers for pseudo-free circle actions, to appear in the 1st issue of 2019 in Journal of Symplectic Geometry.
    (with Yunhyung Cho(SKKU))
  2. Legendrian singular links and singular connected sums, to appear in the 4th issue of 2018 in Journal of Symplectic Geometry.
    (with Youngjin Bae(RIMS) and Seonhwa Kim(IBS-CGP))
  3. Grid diagrams for singular knots, J. Knot Theory Ramification, 27 (2018), no. 4, 1850023, 43pp.
    (with Hwa Jeong Lee(DGIST))
  4. On the $f$-vectors of Gelfand-Cetlin polytopes, European J. Combin., 67 (2018), 61–77.
    (with Yunhyung Cho(SKKU) and Jang Soo Kim(SKKU))
  5. On the structure of braid groups on complexes, Topology Appl., 226 (2017), 86–119.
    (with Hyowon Park)
  6. A criterion for the Legendrian simplicity of the connected sum, Topology Appl., 204 (2016), 175–184.
  7. Automorphisms of braid groups on orientable surfaces, J. Knot Theory Ramification, 25 (2016), no. 5, 1650022, 32pp.
  8. A family of braids with large conjugacy invariant sets, J. Knot Theory Ramification, 22 (2013), no. 6, 1350025, 20pp.
    (with Ki Hyoung Ko(KAIST))
  9. A family of representations of braid groups on surfaces, Pacific J. Math., 247 (2010), no. 2, 257–282.
    (with Ki Hyoung Ko(KAIST))
preprints and papers in preparation
  1. A Chekanov-Eliashberg algebra for Legendrian graphs, under revision.
    (with Youngjin Bae(RIMS))
  2. Edge stabilization in the homology of graph braid groups, under review.
    (with Gabriel C. Drummond-Cole(IBS-CGP) and Ben Knudsen(Harvard University))
  3. Subdivisional spaces and graph braid groups, under review.
    (with Gabriel C. Drummond-Cole(IBS-CGP) and Ben Knudsen(Harvard University))
  4. Ruling invariants for Legendrian graphs, in preparation.
    (with Youngjin Bae(RIMS) and Tamás Kálmán(TIT))
  5. Cup and shuffle products in the cohomology of configuration spaces, in preparation.
    (with Gabriel C. Drummond-Cole(IBS-CGP) and Ben Knudsen(Harvard University))
others
  1. A family of representations of braid groups on surfaces, Ph.D. Thesis, KAIST (2010).
  2. Security Consideration in Ubiquitous Environments of the Project "iWearCom", Proceedings of Next Generation PC 2005 International Conference, Korea Institute of Next Generation PC (2005), 79–85.
    (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 (2005), 15–20.
  4. Cryptanalysis on braid cryptosystem via the Krammer representation, M.S. Thesis, KAIST (2003).

Invited and contributed Talks

  1. Subdivisional spaces and configuration spaces of graphs, Topology Seminar, May 16, 2018, Tokyo Institute of Technology, Tokyo, Japan.
  2. Formality of configuration spaces of graphs, 2018 KMS Spring Meeting, April 21, 2018, Kyung Hee University, Seoul, Korea.
  3. Knot theory and its generalizations in Contact geometry, IBS 5th year Symposium, August 28, 2017, POSCO International Center, Pohang, Korea.
  4. Configuration spaces of graphs, Computational and Algorithmic Topology, Sydney 2017 (CATS2017), University of Sydney, June 27, 2017, Sydney, Australia.
  5. An introduction to braid theory, 2017 Inchon University Math. Dept. Colloquium, Inchon National University, May 8, 2017, Inchon, Korea.
  6. Configuration spaces of graphs, 2017 KMS Spring Meeting, Chosun University, April 29, 2017, Gwangju, Korea.
  7. Configuration spaces of graphs, Topology Seminar, DGIST, April 6, 2017, Daegu, Korea.
  8. An introduction to Braid theory, UGRP Seminar, DGIST, April 5, 2017, Daegu, Korea.
  9. DGA invariant for Legendrian graphs, The 2nd Shinchon Workshop on Algebraic Geometry (SWAG 2), Yonsei University, February 27, 2017, Seoul, Korea.
  10. On the $f$-vectors of Gelfand-Tsetlin polytopes, OCAMI Topology Seminar, Osaka City University, February 20, 2017, Osaka, Japan.
  11. Grid diagrams for singular links, The 12th East Asian School of Knots and Related Topics, University of Tokyo, February 13, 2017, Tokyo, Japan.
  12. DGA invariants for Legendrian spatial graphs, The 2nd Mini workshop on knot theory, IBS-CGP, December 17, 2016, Pohang, Korea.
  13. $f$-vectors for Gelfand-Cetlin polytope, Combinatorics seminar, KIAS, September 8, 2016, Seoul, Korea.
  14. Chekanov-Eliashberg algebra for Legendrian singular links, Low-dimensional topology seminar, Chung-Ang university, August 29 2016, Seoul, Korea.
  15. Chekanov-Eliashberg algebra for Legendrian singular links, Knots in hellas 2016, International Olympic Academy, July 19 2016, Ancient Olympia, Greece.
  16. $f$-vectors for Gelfand-Cetlin polytope, KPPY Combinatorics seminar, Pusan University, April 30, 2016, Busan, Korea.
  17. Chekanov-Eliashberg algebra for Legendrian singular links, Topology Seminar, Hannam University, April 27, 2016, Daejeon, Korea.
  18. Grid diagrams for singular knots, Konkuk University Topology Seminar, March 11, 2016, Seoul, Korea.
  19. On the Chern numbers of pseudo-free circle actions, Seoul National University Topology Seminar, February 12, 2016, Seoul, Korea.
  20. Grid diagrams for singular knots, KAIST Topology Seminar, February 11, 2016, Daejeon, Korea.
  21. On the Chern numbers of pseudo-free circle actions, KIAS Topology Seminar, January 19, KIAS, Korea.
  22. 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.
  23. Grid diagrams for singular knots, Knots and Spatial Graphs 2015, November 5--7, 2015, Daejeon, Korea.
  24. Grid diagrams for singular knots, T-Seminar, October 6, 2015, Postech, Korea.
  25. Legendrian singular links and singular connected sums, Korean-French Conference in Mathematics, August 27, 2015, POSTECH, Korea.
  26. Criterion for the Legendrian simplicity of connected sum of knots, 2015 KMS Spring Meeting, April 25, 2015, Busan, Korea.
  27. Legendrian singular links and singular connected sums, KAIST Topology Seminar, March 24, 2015, KAIST, Korea.
  28. 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.
  29. Braid groups on CW complexes, KIAS Seminar, August 20, 2014, KIAS, Korea.
  30. Braid Functor, Low Dimensional Topology and Related Topics, July 26, 2014, KAIST, Korea.
  31. Braid groups on CW complexes, KAIST Math. Seminar, Feb 3--5, 2014, KAIST, Korea.
  32. Braid groups on CW complexes, The 1st IBS Research Conference, November 27--28, 2013, Daejeon, Korea.
  33. Braid groups on CW complexes, Center for Geometry and Physics Seminar, August 1, 2013, IBS-CGP, Korea.
  34. Braid groups on CW complexes, T-Seminar, May 16, 2013, Postech, Korea.
  35. Automorphisms of braid groups on orientable surfaces, The 9th East Asian School of Knots and Related Topics, January 15, 2013, University of Tokyo, Japan.
  36. Automorphisms of surface braid groups, 2012 KMS Fall Meeting, October 4, 2012, DCC, Daejeon, Korea.
  37. On the structure of braid groups on complexes, PMI Workshop, June, 2012, Pusan, Korea.
  38. On the structure of braid groups on complexes, Colloquium of Math. dept., May 18, 2012, Chung-Ang University, Korea.
  39. Geometric automorphisms of braid groups on surfaces, The 8th East Asian School of Knots and Related Topics, January 9, 2012, KAIST, Korea.
  40. On the structure of braid groups on complexes, Colloquium of Math. dept., December 16, 2011, Chonbuk National University, Korea.
  41. Geometric automorphisms of braid groups on surfaces, KAIST Topology seminar, December 13, 2011, KAIST, Korea.
  42. On injectivity of braid functor, 2011 KMS Fall Meeting, October 21, 2011, Kyungpook National University, Daegu, Korea.
  43. When does $\mathbf{B}_n(X)$ determine $X$?, PMI Annual workshop, September 23, 2011, Postech, Korea.
  44. A family of representations of braid groups on surfaces, Invited Talk, August 23, 2011, KIAS, Korea.
  45. Braid groups on finite cubical complexes, The 7th East Asian School of Knots and Related Topics, January 12, 2011, Hiroshima University, Japan.
  46. Braid groups and their representations, T-Seminar, April 07, 2010, Postech, Korea.
  47. Questions on braid groups, POSTECH Math Department / BK21 / PMI Faculty, Researchers, & Graduate Students Workshop, February 22, 2010, Novotel Ambassador Hotel, Busan, Korea.
  48. 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.
  49. 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.
  50. Representations of braid groups on surfaces, The 3rd East Asian School of Knots, Links and Related Topics, February 8, 2007, Osaka city university, Japan.
  51. 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.
  52. Attack on BDHP via Krammer representation and linear algebra, The 10th Japan-Korea School of Knots and Links, February 21, 2003, Tokyo university, Japan.

Other Activities

Conferences (co)organized
  1. Organizer, 2017 Pohang Mathematics Workshop, December 7–10, 2017, IBS-CGP.
  2. Organizer, The 3rd Mini Workshop on knot theory, June 16–17, 2017, Korea University.
  3. Organizer, The 2nd Mini Workshop on knot theory, December 16–17, 2016, IBS-CGP.
  4. Organizer, Mini Workshop on knot theory, August 19–20, 2016, IBS-CGP.
  5. Organizer, Pohang Mathematics Workshop, November 15–17, IBS-CGP.
  6. Organizer, Friday Workshop of Geometry of Artin Groups, Fall 2012, KIAS/KAIST.
  7. 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–Present.