Diophantine Approximation [Fall 2019]


Algebra: basic group theory, rings, field extensions and Galois theory; Knowledge of Galois theory is convenient but can also be acquired during the course

Aim of the course

Diophantine approximation deals with problems such as whether a given number is rational/irrational, algebraic/transcendental and more generally how well a given number can be approximated by rational numbers or algebraic numbers. Techniques from Diophantine approximation have been vastly generalized, and today they have many applications to Diophantine equations, Diophantine inequalities, and Diophantine geometry. Our present plan is to discuss the following topics (but this may be subject to changes):

  • - geometry of numbers and Minkowski's convex bodies theorems
  • - transcendence results
  • - approximation of algebraic numbers by rationals, including Roth's theorem and Schmidt's subspace theorem if time permits


Jan-Hendrik Evertse (Leiden), Damaris Schindler (Utrecht)