Morse polynomials and Galois theory

Wed, 02/04/2014 - 10:30
Speaker: 
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.