- Notes for Algebraic Spaces and Stacks by M. Olsson: (Not finished yet. Update at 2022/09/13) I take some notes and add some details about the book Algebraic Spaces and Stacks written by Prof. Martin Olsson, aiming to study some basic theory of algebraic stacks.
- Notes of blowing up of schemes: (In Chinese. Not finished yet. Update at 2022/09/03) I wrote the basic theory of blowing up of schemes including some commutative algebra (Rees algebra), blow-ups and strict transform, U-admissible blow-up and its extension and I also gave a introduction and statement of resolution singularities of char=0 by Hironaka. Finally we gave some examples.
- Errata and Notes for Illusie’s Topics in Algebraic Geometry: (Finished yet at 2022/03/28) We will fix some typo and errors in this book and take some notes in this file. I omitted the subsection I.4.14, the section III.4 and the chapter IV! The original book see Illusie.
- Review of Basic Algebraic Topology: (Finished yet at 2023/12/28) This is a review of basic algebraic topology including the first three chapter of A. Hatcher’s book, including fundamental groups, covering spaces, homology and cohomology theory. Moreover we give some proofs of some famous topology theorems, such as Jordan curve theorem, Jordan-Brouwer separation theorem and orientation of compact hypersurface in $\mathbb{R}^n$.
- Some Notes for Goertz and Wedhorn’s AGI book 2nd Edition: (Not finished yet. Update at 2022/02/20) This is a note which aims to fix some gaps in it. The original book see UT1. Its official errata see Errata and Addenda for Algebraic Geometry I (I also upload some errata in this website and this book is very nice).
- Spectral Sequences: (Finished yet) This is a note about the basic spectral sequences. We first discuss the spectral sequences of exact couples, filered complexes and double complexes. Moreover, we will make some examples to show how them work. Furthermore, we also introduce Cartan-Eilenberg Resolutions and its most important application, Grothendieck spectral sequences (We have proved it in the notes!) and its applications such as Leray spectral sequences and so on.
- Notes on Basic Complex Geometry: (Finished yet, the language is Chinese here) This notes is about basic Complex Geometry including the most basic Hodge theory, some vanishing theorems, Kodaira’s embedding theorem and Riemann-Roch theorem.
- Notes on Very Basic Complex Hodge Theory: (Finished yet) This notes is about basic Complex Hodge Theory.
- (2022 Spring) Seminar of Algebraic Geometry and Rigid Geometry We used the notes form Yichao Tian about Rigid Geometry (Actually I didn’t read the rigid geometry part of this seminar). I will write a notes about some basic facts of Derived Categories in Algebraic Geometry. My notes: Derived Categories and Algebraic Geometry.
- (2022 Spring) Seminar of Symplectic Geometry We discuss the second chapters of D. Macduff and D. Salamon’s Introduction to Symplectic Topology and the Chapter 1-7 in Ana Cannas da Silva’s book. One of my lecture: Moser’s trick.
- (2021 Autumn) Seminar of Algebraic Topology We discuss the first two chapters of R. Nott and L. W. Tu’s Differential Froms in Algebraic Topology. I discussed the section 5 and the half of section 11. Here is my lectures:
My Lectures: (1) Section 5;
(2) Section 11.
- (2020 Autumn) Seminar of Homological Algebra We discuss the chapter 5-8 of J.J. Rotman’s An Introduction to Homological Algebra. I discuss the section 6.1. Here is my lecture notes: Section6.1.
The Stacks Project; Allen Hatcher’s Homepage; J.S. Milne’s Homepage; Ravi Vakil’s Homepage; Wenwei Li’s Homepage; 李文威的主页(中文); USTC Math Resources; Jarod Alper’s Homepage; David Mumford’s Homepage; The Rising Sea;
Kerodon; dzackgarza; The Moduli Space; The Automorphic Project; Graduate Seminar in Harvard. Geometric Representation theory; Derived Algebraic Geometry 2022; Patrick Lei’s Notes;
Algebraic Geometry II, Summer semester 2019 in Bonn; Algebraic Geometry in MIT(18-726); (University of Washington) Math 582C: Introduction to stacks and moduli;