Sungkyung Kang
Hello World!
My name is Sungkyung Kang. I am a Titchmarsh Research Fellow in Mathematical Institute, University of Oxford, from Sep 01, 2023.
Here is my CV. I've graduated from Oxford in July 2019. My PhD supervisor was Andras Juhasz.
If you need to contact me, please send an email to sungkyung3838(at)gmail-com. Please don't write me via previous icloud mail account as it is a bit unreliable.
Upcoming Talk/Travel
May 20-24, 2024 Georgia Topology Conference, University of Georgia
Jun 3-14, MATRIX-IBSCGP workshop, IBS Center for Geometry and Physics
Someday early July, visiting IBS CGP again, together with Monica Jinwoo Kang
Jul 21-26, Topologie, Oberwolfach
Sep 1-31, visiting Max Planck Institute of Mathematics
Academic positions
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
Research
I'm interested in using Heegaard Floer theory (and other related techniques) to solve low-dimensional topological problems.
My favorite tool is involutive Heegaard Floer homology.
My papers:
Invariant splitting principles for the Lipshitz-Ozsvath-Thurston correspondence, joint with Gary Guth
Central extensions of higher groups: Green-Schwarz mechanism and 2-connections, joint with Monica Jinwoo Kang
Doubled disks and satellite surfaces, joint with Gary Guth, Kyle Hayden, and Junghwan Park
Topologically and rationally slice knots, joint with Jennifer Hom and Junghwan Park
One stabilization is not enough for closed knotted surfaces, joint with Kyle Hayden and Anubhav Mukherjee
One stabilization is not enough for contractible 4-manifolds
The (2,1)-cable of the figure-eight knot is not smoothly slice, joint with Irving Dai, Junghwan Park, Abhishek Mallick, and Matthew Stoffregen
This preprint was featured in Quanta Magazine. See "outreach" section
Torsion in the knot concordance group and cabling, joint with JungHwan Park, to appear in Journal of European Mathematical Society (JEMS)
Involutive knot Floer homology and bordered modules, to appear in Quantum Topology
Stabilization and satellite construction of doubly slice links, joint with Seungwon Kim and Hongtaek Jung
On the nonorientable four-ball genus of torus knots, joint with Fraser Binns, Jonathan Simone, and Paula Truöl
Linear independence of rationally slice knots, joint with Jennifer Hom, Junghwan Park, and Matthew Stoffregen, Geometry & Topology 26.7 (2023): 3143-3172.
Concordance invariants and the Turaev genus, joint with Seungwon Kim and Hongtaek Jung, International Mathematics Research Notices
Ribbon knots, cablings, and handle decompositions, joint with Jennifer Hom and Junghwan Park, Mathematical Research Letters, Vol. 28, No. 5 (2021), pp. 1441-1457.
Link homology theories and ribbon concordances, Quantum Topology 13.1 (2022): 183-205.
Connected Floer homology of covering involutions, joint with Antonio Alfieri and Andras Stipsicz, Mathematische Annalen, 2020, 377.3: 1427-1452
Z2-equivariant Heegaard Floer cohomology of knots in S3 as a strong Heegaard invariant
A transverse knot invariant from Z2-equivariant Heegaard Floer cohomology
Spectral order for contact manifolds with convex boundary, joint with Andras Juhasz, Algebr. Geom. Topol. 18 (2018) 3315-3338
Works in progress:
The (2n,1)-cable of the figure-eight knot is not slice, joint with JungHwan Park and Masaki Taniguchi
A Heegaard Floer analogue of real-equivariant Seiberg-Witten Floer theory, joint with Anubhav Mukherjee and Masaki Taniguchi
Infinite-order exoticness of Dehn twists along Seifert homology spheres, joint with JungHwan Park and Masaki Taniguchi
Some work going on, joint with my sister, Monica Jinwoo Kang, and Johan Asplund
Outreach
Mathematicians Eliminate Long-Standing Threat to Knot Conjecture, Quanta Magazine, Feb 2023
An interesting open question
Is there a Z/2Z-homology 3-sphere which is not Z/2Z-homology cobordant to branched double covers of S^3 along a knot?
I've been investigating this problem for almost two years, but still have no clue. Maybe equivariant Heegaard Floer homology of Hendricks-Lipshitz-Sarkar can help?
Programming
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.
Teaching
Tutor - Algebraic Topology, University of Oxford, Michaelmas 2023
Tutor - Linear Algebra(Prelims), Keble College, University of Oxford, Michaelmas 2023
The list of teaching experiences I had before the current term is as follows. Note that the Korean law prevented me from teaching classes while doing an alternative military service (i.e. my previous position at IBS).
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
Past Plenary Talks
East Asian Conference on Geometric Topology, Soochow University, China (via Zoom), Feb 2023
Past Invited Talks
Topology Seminar, KAIST, South Korea, April 2024
Differential Topology '24, Tsukuba University, Japan, March 2024
Seminar in Simons senester, IMPAN Warsaw, March 2024
Colloquium, Center for Mathematical Physics Hamburg, January 2024
Topology Seminar, University of Oxford, January 2024
Virtual seminar on geometry and topology, KIAS, South Korea, August 2023
Special session in low-dimensional topology, KMS Spring Meeting, South Korea, April 2023
Mini-workshop on low-dimensional topology, POSTECH, South Korea, April 2023
Gauge Theory in Kyoto, Kyoto University, Japan, March 2023
Informal seminar during a focus week, Alfréd Rényi Institute of Mathematics, Hungary, March 2023
Interactions of 3- & 4-dimensional Topology, China (via Zoom), March 2023
Algebraic Geometry and Differential Topology seminar, Alfréd Rényi Institute of Mathematics, Hungary, March 2023
Knot Online Seminar K-OS, Feb 2023
Morphisms in Low Dimensions, Oberwolfach, Germany, Jan 2023
Moscow-Beijing Topoolgy Seminar, Tsinghua University, China (via Zoom), Jan 2023
Taubes' secret seminar, United States (via Zoom), December 2022
Taubes' secret seminar, United States (via Zoom), November 2022
Floer homotopical methods in low dimensional and symplectic topology, MSRI, United States, November 2022
PK^2 workshop, Busan, South Korea, November 2022
Rookies Pitch seminar, Seoul National University, South Korea, November 2022
Geometry and Topology seminar, Caltech, United States, October 2022
IBS-CGP 10th anniversary workshop, Pohang, South Korea, October 2022
Topology Seminar, Princeton University, United States, September 2022
Topology Seminar, Tokyo University, Japan (via Zoom), July 2022
Topology Seminar, Michigan State University, United States, June 2022
Geometry and Topology Seminar, Rutgers University (via Zoom), April 2022
Workshop for young mathematicians in Korea, South Korea (via Zoom), January 2022
Pohang Mathematical Workshop, Busan, South Korea, December 2021
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, South Korea (via Zoom), April 2021
Special Session on Low-dimensional Topology, KMS Fall Meeting(via Zoom), 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, IBS-Center for Geometry and Physics, South Korea, December 2019
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
East Asian Conference on Geometric Topology, RIMS, Japan, February 2024
Lightning talk, Morphisms in Low Dimensions, Oberwolfach, Germany, January 2023
Workshop for Young Mathematicians in Korea, KAIST, South Korea, December 2022
Lightning Talk, New Perspectives in Four Dimensions, University of Victoria, June 2022
East Asian Conference on Geometric Topology, KIAS, Korea (via Zoom), January 2022
East Asian Conference on Geometric Topology, University of Tokyo, Japan (via Zoom), January 2021
East 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
References
Professor Andras Juhasz, Mathematical Institute, University of Oxford
Professor Ciprian Manolescu, Department of Mathematics, Stanford University
Professor Jennifer Hom, School of Mathematics, Georgian Institute of Technology
Professor Yong-Geun Oh, IBS Center for Geometry and Physics / Pohang University of Science and Technology (POSTECH)
Professor JungHwan Park, Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST)
(Regards Teaching) Dr Richard David Wade, Mathematical Institute, University of Oxford
Miscellaneous
Hamsters are my favorite animals. So cute..........