Computations of Galois groups and Splitting Fields

Nicole Sutherland
University of Sydney
https://www.maths.usyd.edu.au/ut/people?who=NJ_Sutherland&sms=y

Date(s) : 12/09/2019   iCal
11 h 00 min - 12 h 00 min

The Galois group of a polynomial is the automorphism group of its splitting field. The Galois group of a polynomial can be used to compute a splitting field of a polynomial and this was implemented in Magma by Claus Fieker for polynomials over number fields a little over 10 years ago. I will describe the Fieker-Klueners algorithm for computing Galois groups and how similar approaches can be used to compute splitting fields in 3 representations. My interest in these algorithms is to adjust them for use with polynomials over global function fields and I will discuss progress towards this.

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