Research

My research is centered on theoretical mathematics. My main interests are algebraic topology, finite group theory, equivariant homotopy theory, and formal proof. I also maintain a secondary interest in machine learning theory, approached through mathematical structure rather than engineering deployment.

Algebraic Topology and Equivariant Homotopy Theory

I am interested in fixed point methods and homotopical reconstruction. Current themes include:

  • geometric fixed point tomography;
  • spoke Bökstedt periodicity;
  • equivariant fixed point methods;
  • stable homotopy-theoretic structures.

Finite Group Theory and Quillen-Type Problems

I study finite groups through subgroup complexes and local group-theoretic structure. Current themes include:

  • Quillen’s p-subgroup conjecture;
  • centralizer energy methods;
  • FRUL-WOS sphere methods;
  • centralizer and p-local subgroup structures.

Formal Proof and Lean

I am interested in Lean formalization as mathematical infrastructure. My current focus is on Lean, Mathlib, proof engineering, and the formalization of advanced arguments in algebra, topology, and analysis.

Machine Learning Theory

My machine learning theory interests are mathematical rather than engineering-oriented. I focus on generalization, learnability, out-of-distribution prediction, and Koopman/operator-theoretic methods for long-sequence data.

Applied Mathematical Modeling Experience

  • Jingzhou epidemic prevention and population mobility modeling · 2023-2025
    Worked with Prof. Qingpeng Ran on mathematical modeling and statistical surveys related to epidemic prevention and population mobility.

  • Spatial omics data processing · 2025-2026, first half
    Worked with Dayu Hu, Northeastern University, on data processing for spatial omics.

  • Epilepsy and long-sequence data · 2025-2026, second half
    Studied epilepsy-related data and long-sequence modeling in Prof. Huaguang Gu’s group, focusing on Koopman operator methods.