School of Mathematical Sciences

An application of Galois Theory: characterizing solvable polynomials. menu

An application of Galois Theory: characterizing solvable polynomials.

Speaker: 
Diego Millan Berdasco
Date/Time: 
Tue, 28/11/2017 - 16:00
Room: 
Scape 3.01

Nowadays it is well known that there is no general solution by radicals for a polynomial f with arbitrary coefficients (lying in a field characteristic 0) when deg(f)>4. This was proved by Abel using Galois Theory. We will start by giving a brief introduction to this theory which will then use to show the cases in which a polynomial of degree 5 is solvable by radicals. If time allows it, we will also work out a characterisation on solvable quintics in terms of the resolvent and the discriminant associated with the polynomial.