#### About me:

I am currently a Hans Rademacher Postdoc at the University of Pennsylvania, in the mathematical physics group, and am working with Angela Gibney and Daniel Krashen and their students. I was formerly a graduate student at the University of California, Santa Cruz (2018-2023), working under the guidance of Chongying Dong. Here is my CV.

#### Contact Information:

Email (primary): jliu230@sas.upenn.edu

Email (secondary): jliu230@ucsc.edu

Office: DRL 4C3

Phone number: +1 551-334-9439

## Research

My research is in vertex operator algebras (VOAs) and 2D-conformal field theory (CFT). So far, I have been focused on the algebraic side of these theories. I was studying the fusion rules for VOAs and CFTs, Zhu’s algebra, Borel-type subalgebras, classical Yang-Baxter equations, and Rota-Baxter operators for VOAs for my Ph.D. dissertation. Now I am hoping to explore the geometric side of these theories and their deeper connections with physics.

Here are some of my research papers:

- Quasi-triangular decomposition and induced modules for vertex operator algebras,
- Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbifold curves, (with Xu Gao and Yiyi Zhu) arXiv:2403.00545
- Borel-type subalgebras of the lattice vertex operator algebra, arXiv:2402.02278
- Twisted restricted conformal blocks of vertex operator algebras I: g-twisted correlation functions and fusion rules, (with Xu Gao and Yiyi Zhu) arXiv:2312.16278
- On Rota-Baxter vertex operator algebras, (with Chengming Bai, Li Guo, and Xiaoyan Wang)
*J. Pure Appl. Alg., in revision.*arXiv:2307.09826 - Classical Yang-Baxter equation for vertex operator algebras and its operator forms, (with Chengming Bai and Li Guo)
*J. Algebra, in revision.*arXiv:2307.01977 - Endomorphism property of vertex operator algebras over arbitrary fields, (with Chao Yang)
*J. Algebra***622**(2023), 450–468. arXiv:2211.16573 - A proof of the fusion rules theorem,
*Comm. Math. Phys*.**401**(2023), no. 2, 1237–1290. arXiv:2009.14622 - Noetherianity of Zhu’s algebra and bimodules , arXiv:2103.08090

## Teaching

I taught the following courses at UPenn and UCSC:

At the University of Pennsylvania:

- Math 3710 – Algebra II – Fall 2024
- Math 3710 – Algebra II – Spring 2024
- Math 5030 – Algebra II (Master level) – Spring 2024
- Math 1410 – Calculus II – Fall 2023

At the University of California, Santa Cruz (as a graduate student instructor):

- Math 110A – Introduction to Number Theory – Summer 2022-02
- Math 110A – Introduction to Number Theory – Summer 2022-01
- Math 110A – Introduction to Number Theory – Summer 2021-02
- Math 110A – Introduction to Number Theory – Summer 2020-02
- Math 110A – Introduction to Number Theory – Summer 2020-01
- Math 103A – Complex Analysis – Spring 2020