Research

Preprints

Publications

1. The Jacobian of a Sixth-Root-of-Unity Matroid
   With Matthew Baker and Changxin Ding. Annals of Combinatorics (To appear).
   ArXiv
   Abstract

   The Jacobian group (also called the sandpile group, Picard group, or critical group) of a graph or, more generally, of a regular matroid has been well studied. Sixth-root-of-unity matroids, also called complex unimodular matroids, are generalizations of regular matroids. This paper provides a definition, and establishes some basic properties, of the Jacobian group of a sixth-root-of-unity matroid.

2. Machine Learning and LLM-Boost Symbolic Regression for Predicting \(\mathbb{Q}\)-Gonality of Modular Curves With Xiaokang Wang, Yuxiang Yao, Po-Chu Hsu, and Peikai Qi. Accepted at the 2nd AI4MATH@ICML 2025 workshop.

   OpenReview GitHub
   Abstract

   We aim to predict the \(\mathbb{Q}\)-gonality of modular curves, an invariant measuring the minimal degree of a nonconstant rational map to \(\mathbb{P}^1\). Three machine-learning architectures—Extrem gradient-boosted trees, feedforward neural networks, and transformer-based models—achieve over 90\% exact-match accuracy on existing curves, with more than 89\% of predictions falling within known theoretical bounds. To improve interpretability, we employ an LLM-guided boost symbolic regression pipeline that proposes nonlinear feature combinations and uncovers concise analytic formulas. These expressions match the predictive power of our models while revealing how core arithmetic invariants interact. Our results highlight the effectiveness of combining data-driven prediction with LLM-enhanced symbolic discovery in arithmetic geometry.