Title of the course: Diophantine equations
Instructor: Prof. Piotr Kowalski
Institution: Uniwersytet Wrocławski
Dates: 27 July- 2 August 2026
Prerequisites: Some commutative ring theory
Level: Graduate, advanced undergraduate
Abstract: I will start with describing the connections between the Pythagorean triples and the ring of Gaussian integers. Then, I will explain how to solve Pell’s equation using similar rings of algebraic integers and Dirichlet’s unit theorem. Finally, I will concentrate on the 19th century attempts to prove Fermat’s Last Theorem and the corresponding theory of Dedekind rings.
Language: EN