Date: May 6, 9, 13, 16      Time: 18:40-20:30

Date: May 8, 15       Time: 13:00-14:50

The inverse Galois problem asks whether every finite group can be realised as a Galois group over a given number field.  A programme initiated by Hilbert and Noether relates this question to the arithmetic of unirational algebraic varieties.  This course will be an introduction to the study of rational points on such varieties. After introducing the main problems and known tools for approaching rational points on them, we will apply these tools to solve the inverse Galois problem for nilpotent groups, thus recovering and strengthening a well-known theorem of Shafarevich.