其他资料 / Other stuff

讲义及讲稿 / Lecture notes

• Non-rationality of Cubic Threefold: 2016年10月 中科院数学所 代数几何讨论班 讲稿 / October 2018, informal notes for my talks in Algebraic Geometry Seminar held at AMSS, CAS, which mainly focuses on the paper Intermediate Jacobian of the cubic threefold by C. H. Clemens and P. A. Griffiths. In fact, we don't follow all the constructions and details in this paper, instead, we pick up everything we need in this paper only to give a brief proof of the non-rationality of cubic threefold.
• Derivation, Separable and Lie Algebra: 2016年10月 清华大学丘成桐数学科学中心 线性代数群讨论班 讲稿 / October 2018, informal notes for my talks in Linear Algebraic Group Seminar held at YMSC, THU, which mainly focuses on the Chapter 4 of the book Linear Algebraic Groups by T. A. Springer.
• Lecture on Moduli Space: 2016年秋季 中科院数学所 代数几何讨论班 笔记 / Fall 2017, informal notes taken on the Algebraic Geometry Seminar held at AMSS, CAS, which mainly focuses on the construction of moduli space of semi-stable sheaves.
• Lecture notes on intersection theory: 2017年春季 北京大学 《代数几何选讲：相交理论》课程 笔记 / Spring 2017, informal notes taken on the course Intersection Theory held at Peking University. The note taker is responsible for any inaccuracies.
• Moduli of K3 surface: 2017年5月 中科院数学所 代数几何讨论班 讲稿 / May 2017, informal notes for my talks in Algebraic Geometry Seminar held at AMSS, CAS, which mainly focuses on the construction of (fine or coarse) moduli space of K3 surface.
• Lecture on Etale cohomology: Etale cohomology 读书笔记 / Informal notes while learning Etale cohomology, far from perfectness and completeness.
• Moduli of G-bundle: 2017年10月 中科院数学所 代数几何讨论班 讲稿 / October 2017, informal notes for my talks in Algebraic Geometry Seminar held at AMSS, CAS, which mainly focuses on the construction of moduli space of principal G-bundles.
• Fontaine element in p-adic comparison: 2018年6月 中科院数学所 代数几何讨论班 讲稿 / June 2017, informal notes for my talks in Algebraic Geometry Seminar held at AMSS, CAS, which mainly focuses on the construction of Fontaine element in p-adic comparison theorems.
• Reading notes on stacks: 2018年10月 杜伊斯堡-埃森大学 Stacks讨论班 笔记及讲稿 / October 2018, informal notes for my talks in Seminar on Stacks held at Universität Duisburg-Essen.
• Notes at Luminy Summer School: 2019年8月 卢米尼CIRM暑期学校 笔记 / August 2019, informal notes taken on the Summer School "Buildings and Affine Grassmannian" held at CIRM, Luminy.

译作 / Translations

• Riemann-Hilbert对应的超越方面 ：作为本科论文的一部分进行翻译。

Original: Carlos T. Simpson, Transcendental Aspects of the Riemann-Hilbert Correspondence. Illinois J. Math. 34 (1990), no. 2, 368-391. In partial fulfillment of the requirements for the degree of Bachelor of Science.

• 素数的阴谋：中信出版社，2020年3月出版，ISBN: 978-7-5217-1269-8，欢迎批评指教。

Original: The Prime Number Conspiracy. ISBN: 9780262536356. MIT press & co-published with Quanta Magazine. Edited by Thomas Lin. Nov 2018.

杂项 / Miscellany

• An glimpse of anabelian geometry: Jilong Tong在清华大学丘成桐数学科学中心代数几何讨论班的笔记 / Jilong Tong's lecture in Algebraic Geometry Seminar held at YMSC, THU.

简报选萃 / Presentations

• The Geometry of Curves on the Moduli Space of Stable Bundles: May 21th, 2018, AMSS, CAS, Beijing
• Cubic Surface in P^3: June 10, 2015, BUAA, Beijing
• From Hilbert to Godel: the forever incompleteness: October 26, 2014, BUAA, Beijing

本科论文 / Bachelor's thesis

• P^3中的三次曲面 (导师：孙笑涛 & 陈伊凡，2015)
• 此文较为枯燥，旨在研究P^3中的三次曲面：(1) 在光滑曲面的情形，我们给出了其上存在27条直线的一个完整的初等证明，并描述了其上的格结构，Picard群结构及相交理论；(2) 在奇异曲面的情形， 我们在同构意义下给出了正规奇异曲面的完整分类。
• Cubic surfaces in P^3 (Supervisor: Xiao-Tao Sun & Yi-Fan Chen, 2015)
• This thesis is written in a rather arid style. The main goal is to study cubic surface in P^3: (1) In the smooth case, we give an elementary and self-contained proof of the existence of 27 lines on a smooth cubic surface in P^3. After that, I described the lattice structure, the Picard group and the intersection theory. (2) In the singular case, we present a complete classification of normal singular cubic surfaces.

• 高维球面上康托尔集之补的基本群 (尚待清理) (导师：Pankka Pekka，2015)
• 此文内容完全平凡且众所周知，旨在学习Cech cohomology和Alexander's duality和构造，并了解Antoine's Necklece的构造。
• Fundamental groups of complements of Cantor sets on higher dimensional sphere (Incomplete version) (Supervisor: Pankka Pekka, 2015)
• This thesis is totally trivial and well-known. The main goal is to study Cech cohomology and Alexander's duality, as well as understand the construction of Antoine's Necklece.

硕士论文 / Master's thesis

• 稳定向量丛模空间上的曲线及其几何 (导师：孙笑涛，2018)
• 此文总结了稳定向量丛模空间上的各类曲线，特别的面向是有理曲线和椭圆曲线。特别地，我们在最一般的情形给出了其上小有理曲线的一系列结果。
• The Geometry of Curves on the Moduli Space of Stable Bundles (Supervisor: Xiao-Tao Sun, 2018)
• This thesis is an account of survey on various curves on moduli space of stable vector bundles, especially rational and elliptic curves. In particular, in a full generality, something new about small rational curves on it are given.

于2018年5月21日通过答辩 / Defended on May 21th, 2018

论文评审委员会 / Thesis Review Committee

蔡金星 (北大)，陈亦飞 (中科院)，付保华 (中科院)

Jinxing Cai (Peking University), Yi-Fei Chen (AMSS, CAS), Bao-Hua Fu (AMSS, CAS)

论文答辩委员会 / Thesis Defense Committee

蔡金星 (主席，北大)，陈亦飞 (中科院)，付保华 (中科院)，孙笑涛 (中科院)，郑维喆 (中科院)

Jin-Xing Cai (Chair, Peking University), Yi-Fei Chen (AMSS, CAS), Bao-Hua Fu (AMSS, CAS), Xiao-Tao Sun (AMSS, CAS), Wei-Zhe Zheng (AMSS, CAS)