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).

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

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 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