Talks
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Exploring infinity category via simplicial sets, Graduate topology seminar of Sustech, April 18, 2025,
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Homotopy theory via model categories and their underlying infinity-categories, Graduate topology seminar of Sustech, May 23, 2025
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A general introduction to intersection homology, Sustech 2nd Mathematics workshop, November 1, 2025
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Energy bands and Higgs bundles, Workshop on computer-assisted research in geometry and topology, October 9, 2024 Kunming Tianyuan Mathematics Research Center
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Topology and geometry of singularities, Graduated topology seminar of Sustech, May 21,2024, joint with Wenhui Yang and Chenlu Huang
Organized Workshops
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Workshop on infinite-categories, fall 2023, organized by Yunhao Sun and me
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Small workshop on selected topics in geometry and topology, summer 2024, organized by Chenlu Huang and me.
Tex’ed Writings/Notes
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Homotopy limits and colimits
Abstract
I introduced homotopy limits and colimits via derived functors. -
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 abstrct notions by developing the physical manifestations of two systems: the 1/2-spin system and the two-particle system. -
Visualization for $\pi_1(SO(3)/D_2)$ and rotation of eigenvectors
Abstract
In this article we will visualize $SO(3)/D2$ and $\pi_1(SO(3)/D_2)$ to obtain a nice picture describing rotation of eigenframes. -
Notes on Higgs bundles
Abstract
Introduce definition of Higgs bundles and non-abelian Hodge correspondence.
Handwritten Notes
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Notes on stable homotopy theory
Abstract
Introduce some basic definition 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 -
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 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.
Teaching Experience:
As a teaching assistant at the university, I was required to give a weekly class to help students with review and academic enrichment beyond the regular curriculum.