Department of Mathematics

Caltech, Mail Code 253-37

Pasadena, CA 91125

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.

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).

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 $F_K$

A piece of recreational mathematics I did back in 2013

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.

- A note for FAQFT learning seminar (Will be updated as the seminar goes on)

- Introduction to $F_K$ : Caltech Math Graduate Student Seminar, November 6, 2019
- Introduction to topological strings : student presentation in string theory class, April 22 and 24, 2019
- Introduction to homological blocks ($\hat{Z}_b$) : Caltech Math Graduate Student Seminar, April 19, 2019
- Introduction to Chern-Simons theory : Caltech Math Graduate Student Seminar, October 12, 2018

2. Modularity in Quantum Systems. KITP. Oct 26-Dec 18, 2020.

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.