My current research interests span machine learning and statistics, from theory to applications, including large language models, statistical learning theory and deep learning theory.

During my doctoral studies under the supervision of professor Nikolai Makarov, I worked on probability theory, focusing on the mathematical description of random curves and their interactions. In particular, I developed a theory for multiple Schramm–Loewner Evolution (SLE) systems and studied their deterministic limits, exploring the evolution of interacting random curves and their behavior in the limit as randomness vanishes.

At the beginning of my Ph.D., I also worked with professor Rupert Frank on partial differential equations and optimization. I studied energy minimization problems arising from nonlinear diffusion and nonlocal interactions, focusing on the structure of their equilibrium states.

Education

• Ph.D. in Mathematics, California Institute of Technology, 2025
• B.S. in Mathematics, Peking University, 2019
• Visiting Student, Massachusetts Institute of Technology, 2018

Research

• Deep Learning Theory
• LLM Evaluation

  • MathDB: A Dynamic Evaluation Platform for Frontier AI in Research Mathematics at Scale, Shaowu Zhang*, Jiaxin Zhang*, Warren Zhou*, Alexander Du*, Robert George, Haosen Wu, Tony Yue Yu, 2026

    MathDB Database is developed by Caltech math department and currently supported by Meta AI. My contributions include building the Lean database and formal verification infrastructure.

  • GAUSS: Benchmarking Structured Mathematical Skills for Large Language Models, Yue Zhang*, Jiaxin Zhang*, Qiuyu Ren, Tahsin Saffat, Xiaoxuan Liu, Zitong Yang, Banghua Zhu, Yi Ma, 2025.

• Probability Theory and Analysis
  • On the paucity of lattice triangles, David Angdinata, Evan Chen, Ken Ono, Jesse Thorner, Jiaxin Zhang, Jujian Zhang, 2026.
  • Multiple chordal SLE(0) and classical Calegero-Moser system, Jiaxin Zhang, 2025
  • Multiple chordal SLE($\kappa$) and quantum Calegero-Moser system, Jiaxin Zhang, 2025.
  • Multiple radial SLE(0) and classical Calegero-Sutherland system, Jiaxin Zhang, 2024.
  • Multiple radial SLE($\kappa$) and quantum Calegero-Sutherland system, Jiaxin Zhang, 2024.

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