Time: 13:30-15:55, Every Tuesday of Spring 2025 Semester
Venue: E10-312
Course Description:
The course is designed to give a first glance of the modern Diophantine Geometry.
We will study, at an elementary level, the integer solutions to some certain Diophantine equations, the approximation to algebraic numbers by rational numbers. Further, we will study the proof of Thue’s theorem, towards the proof of Roth’s theorem (no proof). We will introduce the height machinery over number fields and projective spaces. Heights lead to the study of S-units equation, the baby case of the celebrated Mordell’s conjecture. For a special case, we discuss the behavior of heights on tori and Zhang’s theorem of small points. We will also give proofs of S-units equation theorem. If time permits, extra topics will be discussed.
Students with ambition in number theory will have a big picture of the current progress of Diophantine geometry, and how other branches in number theory were developed from Diophantine problems.
Students are expected to attend in-person lectures, which is conducted mainly by chalk and board. A reasonable amount of homework/exams will be assigned.
