Teaching

Fall 2022

  • An Introduction to Diophantine Geometry
    • Tutor: Dr. Hang Fu
    • Language: English
    • Twice per week for the main lectures, and once per week for the Exercise Class.
    • The goal of this course is to give an introduction to the height theory and to see some applications. We will include the proof the celebrated Roth's Theorem in the course. Then as topics we will prove the Schinzel-Zassenhaus Conjecture (Dimitrov's Theorem) and the finiteness of integral points on elliptic curves (Siegel's Thoerem).
    • The contents of the course are divided into six parts: Heights on Projective and Affine SpacesSiegel LemmaRoth's TheoremSchinzel-Zassenhaus Conjecture, Height Machine, Integral points on elliptic curves. Lecture notes will be updated after each lecture.
    • The exam is oral and will on the first three chapters.

  • Weekly Seminar: Number Theory and Arithmetic Geometry

Spring 2022

  • Algebraic Groups
    • Tutor: Dr. Jinzhao Pan
    • Language: English
    • Twice per week for the main lectures, and once per week for the Exercise Class.
    • The goal of this course is to give an introduction to algebraic groups. We follow the standard textbook "Linear Algebraic Groups" of A.Borel (GTM 126) and will cover Chapters I-IV.

  • Weekly Seminar: Number Theory and Arithmetic Geometry

Fall 2021

  • An Introduction to Diophantine Geometry
    • Tutor: Dr. Guy Fowler
    • Language: English
    • Twice per week for the main lectures, and once per week for the Exercise Class.
    • The goal of this course is to give an introduction to the height theory and to see some applications. The final goals are to prove Roth's Theorem and the Mordell Conjecture (Faltings's Theorem). We follow Vojta's approach for the proof of the Mordell Conjecture and take Bombieri's simplication.
    • The contents of the course are divided into six chapters: Heights on Projective and Affine SpacesSiegel's LemmaRoth's TheoremAbelian VarietiesHeight MachineMordell Conjecture. Lecture notes will be updated after each lecture. Here are the full lecture notes.
    • The exam is oral and focuses on the first three chapters. Most proofs of the last three chapters are not required, but it is important to understand the notions and the statements of the results.

  • Weekly Seminar: Number Theory and Arithmetic Geometry