I am expanding my research into AI, including reinforcement learning, multi-agent, evaluation and benchmarking, with an emphasis on AI for mathematics.

During my doctoral studies under the supervision of professor Nikolai Makarov, I worked on probability theory, where I developed a theory for multiple SLE systems and analyzed their deterministic limits. For background, see the introductory slides by Fields Medalist Stanislav Smirnov.

At the beginning of my Ph.D., I spent some time working on partial differential equations with professor Rupert Frank. I studied equilibria in nonlinear diffusion and nonlocal interaction. For an accessible introduction, see the introductory lectures by Caltech applied math professor Franca Hoffmann.

During my undergraduate studies at Peking University, I was interested in dynamical systems. I spent a semester at MIT studying Teichmüller dynamics. I completed my thesis with Professor Yi Liu at BICMR on virtual homological spectral radii for surface automorphism.

Education

• Ph.D. in Mathematics, California Institute of Technology, 2025
• B.S. in Mathematics, Peking University, 2019

Research

• Teichmüller dynamics
  • On the paucity of lattice triangles, joint with D. Angdinata, E. Chen, K. Ono, J. Zhang, 2026.
• Benchmark

Early Research during my Ph.D.

• Benchmark
  • GAUSS Benchmark (Benchmarking Structured Mathematical Skills for Large Language Models)
    Designed the GAUSS framework, a benchmark that evaluates large language models’ mathematical abilities through skill-based decomposition.
• Multiple SLE systems
  • Multiple radial SLE(0) and classical Calegero-Sutherland system, Jiaxin Zhang, 2024.
  • Multiple radial SLE($\kappa$) and quantum Calegero-Sutherland system, Jiaxin Zhang, 2024.
  • Multiple chordal SLE(0) and classical Calegero-Moser system, Jiaxin Zhang, 2025
  • Multiple chordal SLE($\kappa$) and quantum Calegero-Moser system, Jiaxin Zhang, 2025.

Notes, Reports and Slides

• GAUSS Eval (Human–LLM Judge Consistency Analysis)
• Irregular traces of multiple SLE(0) systems with multiple marked points, supplementary note, Jiaxin Zhang, 2025.
• Asymptotic of Coulomb gas integrals, Temperley-Lieb type algebras and pure partition functions, supplementary note, Jiaxin Zhang, 2025.
• Slides: Multiple radial SLE(0) and classical Calegero-Sutherland system, 2024

Thesis

• On multiple SLE systems and their deterministic limits, Ph. D. thesis, California Institute of Technology, 2025.

Awards

• Silver Award in the Best Thesis Award at the International Congress of Chinese Mathematicians (ICCM), 2025
• S.-T. Yau College Student Mathematics Contest: Silver Medal in Analysis and Differential Equations (3rd Place), 2017; Silver Medal in Team Competition (2nd Place), 2018.

Invited Talks

• Stochastics Seminar, University of Utah, Feb 28 2025
• Probability Seminar, University of Chicago, Jan 31 2025
• Los Angeles Probability Forum, Caltech, May 2 2024
• Analysis Seminar, Caltech, Apr 10 2024
• Graduate student Seminar, Caltech, Jan 28 2022

Teaching

• California Institute of Technology, Teaching Assistant
  • Ma 1c Calculus and Linear Algebra, Spring 2025
  • ACM 216: Markov Chains, Discrete Stochastic Processes and Applications, Winter 2024
  • Ma 121a Combinatorial Analysis, Fall 2024
  • Ma 140a Probability, Winter 2023
  • Ma 102 Differential Equations, Fall 2023
  • Ma 108c Classical Analysis (Complex Analysis), Spring 2023
  • Ma 110b Analysis (Complex Analysis), Winter 2022
  • Ma 121a Combinatorial Analysis, Fall 2022
  • Ma 103 Intro to Probability and Statistics, Winter 2021
  • Ma 102 Differential Equations, Fall 2021
  • Ma 102 Differential Equations, Fall 2020
  • Ma 110a Analysis (Real Analysis), Fall 2020
  • Ma 1c Calculus and Linear Algebra, Spring 2020
  • Ma 1b Calculus and Linear Algebra, Winter 2019
  • Ma 1a Calculus and Linear Algebra, Fall 2019