Welcome to Ziyang ZHU's Homepage!

I am a Ph.D student (2023.09-?) of the School of Mathematical Sciences, Capital Normal University.

Name: 朱子阳 (Ziyang ZHU)
E-mail: subsunzhu@gmail.com; zhuziyang@cnu.edu.cn
Supervisor: 徐飞 教授 (Fei XU, Prof. Dr.)
Research Interests: Number Theory, Arithmetic Geometry, Dynamical System

News:

• [Snooker] New PB alert! 25-point break on March 10, 2026! (25=1+5+1+7+1+4+1+5)
• [Seminar] Arithmetic Topology and Quadratic Forms. 10:00-12:00, Tuesday; 627, No. 2 Teaching Building.
• [Advert] New notes on the Gross-Zagier formula! Refer to Chapter 4 here (Update: 2025-06).

Publications & Preprints:

1. Riemann-Hurwitz Formula for Arithmetic Surfaces. arXiv:2510.08033.
2. Similarity of Matrices over Dedekind Rings. arXiv:2405.08501.  CMT 
Henri Johnston (University of Exeter) pointed out that Conjecture 1 in this paper is Theorem 30.25 in Curtis and Reiner's book "Methods of Representation Theory I: with Applications to Finite Groups and Orders".

Teaching:

Current Courses:
• Abstract Algebra II. 2026 Spring, teaching assistant, undergraduate students, CNU.
Past Courses:  + 
• Arakelov Geometry. 2023 Spring, 48 class hours, graduate students, CNU.  Note 
• Representation Theory. 2022 Fall, teaching assistant, graduate students, CNU.
• Mathematical Analysis II. 2022 Spring, teaching assistant, undergraduate students, CNU.  Quiz 
• Homological Algebra. 2022 Spring, 8 class hours, mini course, JSNU.
• Dynamical Systems. 2021 Fall, 48 class hours, graduate students, CNU.  Note 
• Arithmetic Geometry. 2021 Spring, 48 class hours, graduate students, CNU.  Note 
• Riemann Surfaces. 2021 Spring, 64 class hours, graduate students, CNU.

Lecture Notes:

• A Concise Course in Arakelov Geometry.  +   PDF 
This is the note for my Arakelov geometry course, our goal is to establish the arithmetic intersection theory and introduce some important applications, such as the arithmetic Riemann-Roch theorem and the Gross-Zagier formula. All comments are welcome!
• Representation Theory I: The Case of Finite Groups.  +   PDF 
This note aims to introduce the representation theory of finite groups, including unitary representation, character theory, Fourier transformation, Burnside theorem, induced representations, etc. It can be read on the basis of linear algebra and abstract algebra, but it may be a little boring to read. (Update: 2020-08, Language: Chinese)
• Algebraic Number Theory I: Galois Theory.  +   PDF 
This is a note to introduce Galois theory, including polynomial theory, the fundamental theorem and its applications, infinite Galois extensions and transcendental extensions. You can read it with the foundation of algebra and topology. (Update: 2020-08, Language: Chinese)
• Algebraic Number Theory II: Elliptic Curves and Modular Forms.  +   PDF 
This note is the special introduction of "Riemann Surfaces", it does not involve proof, but mainly introduces the concept of elliptic curves, modular forms, Mordell theorem, B-SD conjecture and other basic contents. (Update: 2022-05, Language: Chinese)
• Algebraic Number Theory III: Tate's Thesis.  +   PDF 
This is the lecture note of the course "Arithmetic Geometry" at CNU, 2021. The main contents include locally compact groups and their representation theory, abstract harmonic analysis, Fourier transformation and Gelfand transformation, Pontryagin duality and Poisson summation formula, profinite groups, adeles and ideles, Tate's thesis, etc. (Update: 2024-03, Language: Chinese)
• Algebraic Number Theory IV: Class Field Theory.  +   PDF 
Class field theory uses the arithmetic properties of a global field to determine all its abelian extensions. There are many ways to prove it, we only introduce Tate's idea, and will not give serious proofs. This is the lecture note of the course "Class Field Theory and Reciprocal Law" at CNU, 2021. (Update: 2022-09, Language: Chinese)
• Algebraic Number Theory VI: Arithmetic Dynamics.  +   PDF 
Dynamical system is a subject that studies the iteration by means of statistics, it also connects to the number theory. This note consists of four topics: ergodic theory, Oppenheim conjecture, entropies and geometric topology of moduli spaces. This is the lecture note of the course "Dynamical Systems" at CNU, 2021. (Update: 2022-10, Language: Chinese)

Events:

Presentations:
• Some Problems on Algebraic Dynamics. Peking University, 2022-07.  Note 
History:  + 
• [Seminar] Capital Normal University. Mathematical Statistical Physics II: Kinetic Theory. 2025-10.  Slide 
• [Seminar] Capital Normal University. Introduction to Automorphic Representations. 2024-03.  Note 
• [Seminar] Capital Normal University. Mathematical Statistical Physics I: Ensemble Theory. 2023-12.  Slide 
• [Lecture] Y.W. Fan, Tsinghua University. Endofunctors of Triangulated Categories from the Dynamical Perspective. 2022-04.
• [Lecture] Z.Y. Liu, Sichuan University. Stability Conditions and Geometry of Fano Threefolds. 2021-12.
• [Lecture] J.Y. Zhao, University of Illinois Chicago. Classification of Algebraic Curves and Riemann Surfaces. 2021-06.

Useful Links:

URL:  arXiv   GeoGebra   LMFDB   Macaulay2   Magma   Mathcha   SageCell   ...