The work I do can be divided into three parts:

• Homotopy theory
• Infinity categories
• Topology of the configuration of eigenvectors and eigenvalues of parametrized Hamiltonians（Preprint）

1.Homotopy theory

1.1 Talks

• Homotopy theory via model categories and their underlying infinity-categories, Graduate topology seminar of SUSTech, May 23, 2025

1.2 Writings/Notes

• Homotopy limits and colimits
  Abstract

  I introduced homotopy limits and colimits via derived functors.
• Notes on homotopy theory
  Abstract

  The main reference of this note is Hatcher's algebraic topology and ch1,2 for this lecture notes.
• Notes on stable homotopy theory
  Abstract

  Introduce some basic definitions in stable homotopy theory, such as spectrum, stable homology theory, stable homotopy category, and so on, which also appear in many other topics. The main reference is link

2.Infinity categories

2.1 Talks

• Exploring infinity category via simplicial sets, Graduate topology seminar of SUSTech, April 18, 2025

2.2 Organized Workshops

• Workshop on infinite-categories, fall 2023, organized by Yunhao Sun and me

3.Topology of the configuration of eigenvectors and eigenvalues of parametrized Hamiltonians

3.1 Preprint

• Topology of the configuration of eigenvectors and eigenvalues of parametrized Hamiltonians
  Abstract

  In this article, we discuss the topological classification of the configuration of eigen vectors and eigenvalues of 2-band and 3-band Hermitian and pseudo-Hermitian Hamiltonians. Besides, this article computes the intersection homology of different parameter spaces to study the topology of the parameter space, which is useful for further work.

The related works are as follows:

3.2.1 Talks

• A general introduction to intersection homology, SUSTech 2nd Mathematics workshop, November 1, 2025
• Energy bands and Higgs bundles, Workshop on computer-assisted research in geometry and topology, October 9, 2024, Kunming Tianyuan Mathematics Research Center
• Topology and geometry of singularities, Graduated topology seminar of SUSTech, May 21, 2024, joint with Wenhui Yang and Chenlu Huang

3.2.2 Organized Workshops

• Small workshop on selected topics in geometry and topology, summer 2024, organized by Chenlu Huang and me

3.2.3 Writings/Notes

• Notes on Higgs bundles
  Abstract

  Introduce the definition of Higgs bundles and non-abelian Hodge correspondence.
• Notes on fiber bundles
  Abstract

  It introduces fiber bundles, principal bundles, classification of principal bundles, and characteristic classes, including Chern classes, Stiefel-Whitney classes, and Pontrjagin classes. It's the note for ch3,4 of this lecture notes.
• Differential geometry of vector bundles (Ch III in Differential Analysis on Complex manifolds)
  Abstract

  It introduces connections, curvatures, and Chern classes.
• Physical picture of tensor products and direct sum
  Abstract

  Tensor products and direct sums of vector spaces are abstract concepts in linear algebra. In this article, we aim to elucidate these abstract notions by developing the physical manifestations of two systems: the 1/2-spin system and the two-particle system.