Notes

Seminar Notes

• Seminar on Higgs bundles and related topics. Here is the seminar note written by Qiliang Luo, Bating Xie and myself, Spring 2025.

• Bridgeland stability and dHYM metric of line bundles on surface (note version). This is my final report for the course “topics in derived categories”, lectured by Yuwei Fan, 2024/11/28.

• Notes on Chern Inequalities. Based on a talk I gave, I discuss the Chern number inequalities of semistable torsion-free sheaves, 2024/05/12.

• Notes on a brief Introduction to Hodge Theory. Based on a talk I gave, I covered a brief introduction to Hodge theory, such as Hodge structure, variation of Hodge structures and differential geometry of Hodge bundles, 2024/04/09.

• Notes on Algebraic de Rham Cohomology. I discuss algebraic de Rham complexes, such as comparison theorems, E1 degenerations of Hodge to de Rham spectral sequences, Spring 2024.

• Seminar on toric variety, and here are some lecture notes: 09-23, 10-07, 10-28, 11-11, 11-18, 12-30, 1-07, Fall 2023.

• Curvatures of left-invariant metrics on Lie groups. Slides on curvature properties of left-invariant metrics on Lie groups, and the main reference is Milnor’s paper, 2023/09/22.

• Review of topology (note version) frequently used in geometry, 2023/06/27.

• Uniqueness of the K"ahler structure of complex projective space (note version). This is my final report for the course “advanced topics in complex geometry”, lectured by Xiaokui Yang, 2023/06/08.

• Principal bundle and its applications. Based on a talk I gave, In this lecture, firstly I introduce principal bundle and connections on it, and then I introduce its applications on Chern-Weil theory, Spring 2023.

• Spectral sequence and its applications. Based on a talk I gave in a seminar series about Bott-Tu’s GTM82, which is organized by Chenglong Yu, Fall 2022.

• Commutative algebra, Summer 2022.

Lecture Notes

• Abelian variety, lectured by Mao Sheng, Spring 2025.

• Five lectures on Introduction to singularities, lectured by Ruijie Yang, and I typed the draft version of it, Summer 2024.

• Algebraic curve, lectured by Chenglong Yu, Fall 2023.

• Representation theory (Draft version), lectured by Emanuel Scheidegger, Spring 2022.

• Homology theory, lectured by Huabin Ge, Spring 2022.

Learning Notes

• Moduli problems of bundles. Draft I typed when I learned moduli problems of bundles, Spring 2025.

• Algebraic geometry. Notes I typed when I learned algebraic geometry from a course taught by Lei Fu, Fall 2023. (Last updated 2024/1/13)

• Symmetric space. Notes I typed about symmetric space, and the main reference is the textbook written by Sigurdur Helgason. (Last updated 2023/09/12)

• Complex geometry I (Draft version). Lecture notes about complex differential geometry. The initial draft of this note is taken in spring 2022 in the course about Hodge theory taught by Qizheng Yin, and that’s my first time to learn this beautiful theory. Later in Spring 2023 I added more useful techniques and advanced topics (such as Schwarz computations, Calabi-Yau theorem and so on) I learnt in the course “advanced topics in complex geometry” given by Xiaokui Yang. I also added some other materials from classical books to make this note self-contained.

• Partial differential equation, Notes I typed when I learned about PDE, and it mainly followed the textbook written by Evans, Fall 2022.

• Riemannian geometry. Notes I typed when I learned about Riemannian geometry from a course taught by Xiaokui Yang in 2022Fall, and from this course I learnt quite a lot, Fall 2022.

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