I am expanding into AI, with a focus on large language models and AI for mathematics.

My research background lies at the intersection of probability theory and partial differential equations (PDEs).

During my Ph.D., I developed a theory for multiple SLE systems —a class of random multi-curve systems—and analyzed their deterministic limits. For background, see the introductory slides by Fields medalist Stanislav Smirnov.

Previously, I also studied equilibria in nonlinear diffusion and nonlocal interaction, focusing on the structure of energy minimizers and connections to optimal transport theory. For an accessible introduction, see the introductory lectures by Caltech applied math professor Franca Hoffmann.

Education

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

Research

• AI for math *
• Large language models
  • Technical Review: Chatbot Arena and Prompt-to-Leaderboard (P2L), 2025.
  • Slides: Chatbot Arena and Prompt-to-Leaderboard (P2L), 2025.
• Multiple SLE systems
  • [Probabilistic and algebraic structures in multiple SLE systems and their deterministic limits: a survey], expository article, Jiaxin Zhang, in preparation.
  • 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.
  • Multiple chordal SLE($\kappa$) and quantum Calegero-Moser system, submitted, Jiaxin Zhang, 2025.
  • Multiple chordal SLE(0) and classical Calegero-Moser system, submitted, Jiaxin Zhang, 2025
  • Multiple radial SLE($\kappa$) and quantum Calegero-Sutherland system, submitted, Jiaxin Zhang, 2024.
  • Multiple radial SLE(0) and classical Calegero-Sutherland system, submitted, Jiaxin Zhang, 2024.
  • 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.

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