My name is Sungkyung Kang. I am a postdoctoral fellow at Institute of Basic Science - Center for Geometry and Physics, situated at Pohang. This job works as an alternative military position for me.
If you need to contact me, please send an email to sungkyung38(at)icloud-com.
Please ignore my previous website, as it is now very outdated and no longer maintained.
2020-present, Postdoctoral Fellow at IBS Center for Geometry and Physics
2019-2020, Postdoctoral Fellow at the Chinese University of Hong Kong
Trinity 2016, Non-stipediary Lecturer, Keble College, University of Oxford
I'm interested in using Heegaard Floer theory (and other related techniques) to solve low-dimensional topological problems.
The topics that I'm mainly currently focusing on include: knot slicing, double slicing and various concordance problems, mainly in the 4D smooth category.
Stabilization and satellite construction of doubly slice links, joint with Seungwon Kim and Hongtaek Jung
Link homology theories and ribbon concordances, to appear in Quantum Topology
Spectral order for contact manifolds with convex boundary, joint with Andras Juhasz, Algebr. Geom. Topol. 18 (2018) 3315-3338
Works in progress:
UV=0 truncated involutive knot Floer homology from (-1)-surgery
Some work going on, joint with my sister, Monica Jinwoo Kang.
Given a quasi-alternating knot, its branched double cover Σ(K) is an L-space. Thus the induced homotopy involution, induced by the deck transformation, on the Heegaard Floer chain complex of Σ(K) is nulhomotopic. Now, if we consider the knot filtration, we get the knot Floer theory of (Σ(K),K), and the deck transformation action here might be nontrivial.
Question (originally by Stipsicz): Can we find an example of such a knot K?
I was working on this question earlier this year. Given a n-by-n grid diagram of K, one can explicitly compute the Z/2-action on the hat-flavored HFK of (Σ(K),K), with space complexity and time complexity O((n!)^2), which is doable when n is at most 9. But for all examples of K that I tested had trivial action on HFK.
If somebody can find an example that works, please let me know!
Here's the C++ code that I wrote to solve this.
The Korean law prevents me from teaching classes while doing an alternative military service (i.e. my current position at IBS). The list of classes I taught before taking the current position is as follows.
Lecturer - Linear Algebra, The Chinese University of Hong Kong, Fall 2019
Tutor - Group Theory, Keble College, University of Oxford, Trinity 2019
Teaching Assistant - Geometric Group Theory, University of Oxford, Hilary 2018
Teaching Assistant - Algebraic Topology, University of Oxford, Michaelmas 2017
Class Tutor, Keble College, University of Oxford, Hilary 2017 - Trinity 2017
Teaching Assistant - Algebraic Topology, University of Oxford, Michaelmas 2016
Teaching Assistant - Algebraic Number Theory, University of Oxford, Hilary 2016
Teaching Assistant - Algebraic Topology, University of Oxford, Michaelmas 2015
Teaching Assistant - Logic and Set Theory, KAIST, Fall 2014
Pohang Mathematical Workshop, Dec 1-4, 2021
Past Invited Talks
Topology Seminar, KAIST, South Korea, October 2021
Recent techniques in Floer and Khovanov homology, NCNGT, June 2021
Special Session on Floer theory, KMS Spring Meeting, April 2021
Special Session on Low-dimensional Topology, KMS Fall Meeting, October 2020
Moscow-Beijing Topology Seminar, Tsinghua University, China (via Zoom), July 2020
Topology Seminar, IMS, CUHK, Hong Kong (via Zoom), July 2020
Mini-Symposium : Knot Theory in Okinawa, OIST, Japan, February 2020
Topology Seminar, KIAS, South Korea, November 2019
Symplectic Geometry Seminar, Stony Brook University, United States, November 2019
Topology Seminar, Boston College, United States, October 2019
Topology Seminar, Georgia Tech, United States, October 2019
Topology Seminar, Institute of Mathematical Sciences, The Chinese University of Hong Kong, September 2019
Topology Seminar, UCLA, United States, July 2019
Topology Seminar, University of Oregon, United States, July 2019
Topology Seminar, KIAS, South Korea, June 2019
Poincare Seminar, University of Oxford, United Kingdom, May 2019
Chekanov-Eliashberg algebra and knot invariants, Alfred Renyi Institute of Mathematics, Hungary, March 2019
Geometry and Topology Seminar, Seoul National University, South Korea, July 2018
Topology Seminar, University of Oxford, United Kingdom, January 2018
Past Contributed Talks
Asian Conference on Geometric Topology, University of Tokyo, Japan (via Zoom), January 2021
Asian Conference on Geometric Topology, RIMS, Japan, February 2020
Short Talk, Floer Homotopy 2019, University of Oregon, United States, July 2019
Early Career Topology Conference, University of Sheffield, United Kingdom, June 2019
Young Researchers in Mathematics 2018, University of Southampton, United Kingdom, June 2018
British and Irish Geometry Meeting 2018, Queen’s University Belfast, United Kingdom, March 2018
Hamsters are my favorite animals. So cute..........