Lehre

Winter 2022

Sommer 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.

  • Oberseminar Zahlentheorie und Arithmetische Geometrie

Winter 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 Spaces, Siegel's Lemma, Roth's Theorem, Abelian Varieties, Height Machine, Mordell 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.

  • Oberseminar Zahlentheorie und Arithmetische Geometrie