LIU JIANQI

Dr. Jianqi Liu's research focuses on Vertex Operator Algebras (VOAs), Representation Theory, Conformal Field Theory, and Algebraic Geometry. His work explores conformal blocks on algebraic curves, the associated vector bundle on the moduli space of algebraic curves, fusion tensor products in the tensor category of VOA modules, and the classical Yang–Baxter equations as well as Rota–Baxter operators for VOAs.

Dr. Liu is currently an Assistant Professor in the Department of Mathematics at New Uzbekistan University. Previously, he was a Hans Rademacher Instructor (Postdoctoral) in the Department of Mathematics at the University of Pennsylvania.

1. University of California, Santa Cruz, Santa Cruz, CA USA (2018–2023) Ph.D. in Mathematics, June 2023
2. – Dissertation: Correlation Functions, Fusion Rules, and the Classical Yang-Baxter Equation of Vertex Operator Algebras.
3. – Advisor: Chongying Dong
4. Qingdao University, Qingdao, Shandong Province, China (2015–2018)
5. M.S. in Pure Mathematics, June 2018
6. Qingdao University, Qingdao, Shandong Province, China (2011–2015) B.S. in Computational Mathematics, Minor in Computer Science, June 2015

University of Pennsylvania, Philadelphia, PA, USA — Hans Rademacher Instructor (Postdoctoral), Department of Mathematics, August 2023–Present.

University of California, Santa Cruz, Santa Cruz, CA, USA — Graduate Student Instructor, 2020–2022.

University of California, Santa Cruz, Santa Cruz, CA, USA — Teaching Assistant, 2018–2023.

Gao, X., Liu, J., Zhu, Y. “Twisted restricted conformal blocks of vertex operator algebras II: twisted restricted conformal blocks on totally ramified orbicurves.” International Mathematics Research Notices, 16 (2026), rnag164.

Bai, C., Guo, L., Liu, J., Wang, X. “On Rota-Baxter vertex algebras.” Journal of Pure and Applied Algebra, 230 (2026), no. 3, 108202.

Liu, J. “One-point restricted conformal blocks and the fusion tensor product.” Mathematische Zeitschrift, 312 (2026), no. 88.

Liu, J. “Borel-type subalgebras of the lattice vertex operator algebra.” Journal of Pure and Applied Algebra, 229 (2025), no. 7, 107999, 36 pp.

Gao, X., Liu, J., Zhu, Y. “Twisted restricted conformal blocks of vertex operator algebras I: g-twisted correlation functions and fusion rules.” Journal of Algebra, 675 (2025), 59–132.

Bai, C., Guo, L., Liu, J. “Classical Yang-Baxter equation for vertex operator algebras and its operator forms.” Journal of Algebra, 671 (2025), 117–158.

Liu, J. “Noetherianity of twisted Zhu’s algebra and bimodules.” Proceedings of the Edinburgh Mathematical Society, 68 (3) (2025), 675–704.

Liu, J. “A proof of the fusion rules theorem.” Communications in Mathematical Physics, 401 (2023), no. 2, 1237–1290.

Liu, J. and Yang, C. “Endomorphism property of vertex operator algebras over arbitrary field.” Journal of Algebra, 622 (2023), 450–468.

Preprints

Gao, X. and Liu, J. “On strong identities of almost-canonically seminormed rings.” arXiv:2606.05965.

Gao, X. and Liu, J. “Trace-function bases and modular symmetry for genus-one VOA conformal blocks.” arXiv:2508.01294.

Liu, J. “Rank-two parabolic-type vertex operator algebras and nilpotency of nil ideals.” arXiv:2508.21662.

Liu, J. “Finite induction functor for vertex operator algebras.” arXiv:2503.23632.