# Morse polynomials and Galois theory

Seminar

Speaker

Dr. Lior Bary-Soroker (Tel Aviv University)

Date

02/04/2014 - 10:30Add to Calendar

`2014-04-02 10:30:00``2014-04-02 10:30:00``Morse polynomials and Galois theory``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.``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`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 Updated Date : 20/03/2014