Sunghyuk “Henry” Park

Department of Mathematics
Caltech, Mail Code 253-37
Email : spark3_at_caltech.edu

I am a graduate student at Caltech studying geometry and topology inspired by supersymmetric QFTs and string theory.
My supervisor is Sergei Gukov.

Here is my curriculum vitae.

Research

So far, I have been mostly working on some mathematical aspects of 3d $\mathcal{N}=2$ theory $T[Y^3]$, especially the half-index $\hat{Z}_b(q)$ (homological blocks).

3d-3d correspondence for mapping tori (with S. Chun, S. Gukov, N. Sopenko), (will appear on arXiv soon)
Higher rank $\hat{Z}$ and $F_K$, arXiv preprint (2019)
In this paper we study $\hat{Z}$ and $F_K$ for arbitrary gauge group, generalizing earlier works by Gukov-Pei-Putrov-Vafa and Gukov-Manolescu. (Any comments welcome!)

Some other ongoing research projects include :

• Large $N$ of $F_K$ and $\hat{Z}$, and relation to enumerative geometry of open topological strings
• Refined $\hat{Z}$ and $F_K$

Other articles

Prague Clocks (with C. Bae, J. Conway, L. Kohlhase), The Mathematical Intelligencer 38, 37 (2016)
A piece of recreational mathematics I did back in 2013

Learning seminar

This term, Tamir Hemo and I are organizing a learning seminar on Factorization Algebras in Quantum Field Theory, following the two-volume book by Costello and Gwilliam.

Travel

Upcoming events

1. Knots, Strings, Symplectic Geometry and Dualities. IML. Sep 1-Dec 11, 2020.
2. Modularity in Quantum Systems. KITP. Oct 26-Dec 18, 2020.

Past events

9. 2019 2nd q-day : q-series and related topics. KIAS. Aug 16, 2019.
8. International Workshop on Arithmetic Geometry and Quantum Field Theory. KIAS. Aug 12-16, 2019.
7. PCMI Summer Session 2019 : Quantum Field Theory and Manifold Invariants. PCMI. June 30-July 20, 2019.
6. New Developments in Quantum Topology. UC Berkeley. June 3-7, 2019.
5. Hidden Algebraic Structures in Topology. Caltech. Mar 13-16, 2019.
4. Modularity and 3-manifolds. ICERM. Mar 8-10, 2019.
3. Between Topology and Quantum Field Theory. UT Austin. Jan 14-18, 2019.
2. CQ3MI Summer School and Workshop. USC. July 16-21, 2018.
1. SMS 2018 : Derived Geometry and Higher Categorical Structures in Geometry and Physics. Fields Institute. June 11-22, 2018.