# Byung Hee An

### 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
Mar. 2003 – Feb. 2010
Ph.D. in Mathematics, KAIST
Thesis: A family of representations of braid groups on surfaces
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 (RIMS), (TIT), (IBS-CGP)
• Papers: in press, under revision and in preparation
• Homotopy invariants of configuration spaces of graphs
• joint with (IBS-CGP) and (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 (SKKU))
2. Legendrian singular links and singular connected sums, to appear in the 4th issue of 2018 in Journal of Symplectic Geometry.
(with (RIMS) and (IBS-CGP))
3. Grid diagrams for singular knots, J. Knot Theory Ramification, 27 (2018), no. 4, 1850023, 43pp.
(with (DGIST))
4. On the $f$-vectors of Gelfand-Cetlin polytopes, European J. Combin., 67 (2018), 61–77.
(with (SKKU) and (SKKU))
5. On the structure of braid groups on complexes, Topology Appl., 226 (2017), 86–119.
(with )
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 (KAIST))
9. A family of representations of braid groups on surfaces, Pacific J. Math., 247 (2010), no. 2, 257–282.
(with (KAIST))
##### preprints and papers in preparation
1. A Chekanov-Eliashberg algebra for Legendrian graphs, under revision.
(with (RIMS))
2. Edge stabilization in the homology of graph braid groups, under review.
(with (IBS-CGP) and (Harvard University))
3. Subdivisional spaces and graph braid groups, under review.
(with (IBS-CGP) and (Harvard University))
4. Ruling invariants for Legendrian graphs, in preparation.
(with (RIMS) and (TIT))
5. Cup and shuffle products in the cohomology of configuration spaces, in preparation.
(with (IBS-CGP) and (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 (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.

### 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.