# Morse polynomials and Galois theory

Wed, 02/04/2014 - 10:30

Speaker:

Dr. Lior Bary-Soroker (Tel Aviv University)

Seminar:

Abstract:

Many problems in algebra and number theory reduce to

the problem of calculating Galois groups.

In this talk, I will focus on the proof of the following theorem:

Thm: Let x |--> f(x) be a polynomial map from the Riemann sphere to itself of degree n=deg f.

Assume that f(x) is Morse (in the sense that the critical points are non-degenerate and the critical values are distinct).

Then the Galois group is the full symmetric group.

The proof involves some geometry and some finite group theory.

- Last modified: 20/03/2014