Note for Riemannian Surface
This is the note on Riemannian surface. The reference textbook is Riemannian Surface by Mei Jiaqiang. The note is divided into two parts since there is a restriction on file size when uploading files on Github.
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Note for Morse Theory
This is the note on Morse Theory. The reference textbook is Morse Theory by J. Milnor.
A Very Brief Note about Symplectic Topology
This is a very very brief note on symplectic topology.
Note on the book Geometry and Analysis on Manifolds
This note is for the book Geometry and Analysis on Manifolds by Zhang Weiping.
Note for Differential Geometry(H) (2024FALL)
Note for the differential geometry course. The lecturer is Prof. Liu Shiping.
Coverage: Chap 1-5,7,8.1-8.3 of Differential Geometry by Chen Qing.
Note for Introduction to Algebraic Geometry I (2024FALL)
Note for the introduction to algebraic geometry course(MATH5016P.01). The lecturer is Prof. Zhanglei
Note for Elliptic PDE
This is a note on ellptic PDE theory, corresponding to the course MATH5009P.
Basic Floer theory in Arnold conjecture
This is the note on the basic Floer theory for solving Arnold conjecture(monotone case). I followed the paper Elliptic Methods in Symplectic Geometry by McDuff. Most details about analysis are covered. One may consult the original papers of Floer for more.
Probability Theory Lecture Note (2023 FALL, Latex typed)
Note for the course “Probability Theory(MATH3007)” of USTC in 2023FA semester. The lecturer is Prof. Dang-Zheng Liu. The note covers all the content in the course, including basic definitions in probability theory, discussion on random variables, law of big numbers and central limit theorem.
Note for Complex Geometry(NOT COMPLETED)
I made this note when learning the video course of complex geometry taught by Prof. Zhang Xi in 2020SP semester. The video can be found here. The note is divided into two parts.
Note for Functional Analysis(H) (2024FALL)
Note for the functional analysis course. The lecturer is Prof. Huang Wen.
Coverage: Chap 1-3 of Lecture Note on Functional Analysis by Zhang Gongqing
A Survey on Kahler-Einstein Metric
This is a brief survey on the problems about Kahler-Einstein metric proposed by Calabi in the 1950s, finally solved by Chen-Donaldson-Sun,Tian in the 2010s.
Note on basics of Ricci flow
This is a note on Ricci flow, based on the content of the course Foundations of Ricci flow taught by Prof. Li Yu.