# A Galois counting problem

### Sam Chow (University of Warwick)

Wednesday 26th February, 2020 16:00-17:00 Maths 311B

#### Abstract

We count monic cubic and quartic polynomials with prescribed Galois group. We obtain the order of magnitude for D_4 quartics, and show that if d \in \{3,4\} then irreducible non-S_d polynomials of degree d are less prevalent than reducible polynomials of degree d. The latter confirms the cubic and quartic cases of a 1936 conjecture of van der Waerden. This is joint work with Rainer Dietmann.