Xianghui Shi

Xianghui Shi

Contact information

  • Email: xhshi@math.ucla.edu
  • Mailing address: Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Box 951555, Los Angeles, CA 90095-1555, USA

About me

I’m a Hedrick Assistant Adjunct Professor in the Department of Mathematics at UCLA.

I received my PhD in Mathematics in 2026 from Peking University, where I was a student at the Beijing International Center for Mathematical Research (BICMR) under the supervision of Professor Zhiqiang Li. I received my BS in Mathematics from Peking University in 2021.

Here is my CV.

Research interests: Dynamical Systems, Complex Dynamics, Ergodic Theory, Thermodynamic Formalism, Statistical Properties, Mathematical Billiards, Quasiconformal Geometry

Publications and Preprints

  • X. Shi, A characterization of planar quasisymmetric embeddability of rectangular carpets. In preparation.

  • Jie Yan†, Maolin Wang†, Junzhong Xie†, Yapeng Zhao†, Xianghui Shi†, Yuxiong Hu, Shixiang Yu, Xingwu Liu, Chaowu Xue, Shuheng Tian, Yaxuan Wang, Zijun Peng, Wu Zhou, Hiroyuki Asakura, Meng Wang, Zhiqiang Li*, Zhu–Jun Wang*, Ding Ma*, Reactive Oxygen Pool over Ceria Enables Catalytic Oscillation. In preparation.

  • X. Shi, Infinitesimal dynamical spectral rigidity of the Bunimovich stadium. Preprint. arXiv:2609.16241. 42 pages.

  • X. Shi (with Zhiqiang Li), Counting prime orbits in shrinking intervals for expanding Thurston maps. Submitted. arXiv:2511.22601. 34 pages. PDF.

  • X. Shi (with Ilia Binder, Qiandu He, Zhiqiang Li), Computable thermodynamic formalism. Submitted. arXiv:2512.01259. 39 pages. PDF.

  • X. Shi (with Zhiqiang Li), Entropy density and large deviation principles without upper semi-continuity of entropy. Submitted, arXiv:2406.01712. 55 pages. PDF.

  • X. Shi (with Zhiqiang Li), Thermodynamic formalism for subsystems of expanding Thurston maps II. Submitted, arXiv:2404.07247. 43 pages. PDF.

  • X. Shi (with Zhiqiang Li, Yiwei Zhang), Thermodynamic formalism for subsystems of expanding Thurston maps and large deviations asymptotics. Proc. Lond. Math. Soc. (3) 130, 2025, e70019. 77 pages. PDF.

Teaching

  • Fall 2026: Math 32B, Calculus of Several Variables, UCLA.