# Sungkyung Kang

Hello World!

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.

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 sungkyung38(at)icloud-com.

**Please ignore my ****previous website****, as it is now very outdated and no longer maintained.**

## 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.

The topics that I'm mainly currently focusing on include: knot slicing, double slicing and various concordance problems, mainly in the 4D smooth category.

**My papers:**

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, to appear in

*Geometry & Topology*

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, to appear in

*Mathematical Research Letters*Link homology theories and ribbon concordances, to appear in

*Quantum Topology*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:**

UV=0 truncated involutive knot Floer homology from (-1)-surgery

Some work going on, joint with my sister, Monica Jinwoo Kang.

## 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

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

## Upcoming Talk/Travel

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, 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

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

## Miscellaneous

Hamsters are my favorite animals. So cute..........