1. Background

Diophantine approximation deals with problems such as whether a given number is rational/irrational, algebraic/trascendental and more generally how well a given number can be approximated by rational numbers or algebraic numbers. In 1842, Dirichlet demonstrated his fundamental theorem in Diophantine approximation: for every real number , there exist infinitely many rational numbers  such that  We call the approximation property asymptotic approximation. Techniques from Diophantine approximation have been vastly generalized, and today they have many applications to Diophantine equations, Diophantine inequalities, and Diophantine geometry.

2. Course Outline

This mini course starts from the fundamental background of Diophantine approximation, and intends to cover some recent developement in many fields.

3. Grading

Homework assigned in class.

4. Date and Time

8/8, 8/12, 8/16 (14:00-17:00, 3hr class), 8/19, 8/22, 8/24

5. Online Course

Link: <Zoom Link to Fractals in Diophantine Approximation>

6. Registration

https://forms.gle/LuxxToNMu1CGyZsQA