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SUMMARY:Invariable generation of finite classical groups - Eilidh McKemmie
  (University of Southern California)
DTSTART:20200130T160500Z
DTEND:20200130T163500Z
UID:TALK138190@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We say a group is invariably generated by a subset if it forms
  a generating set even if an adversary is allowed to replace any elements 
 with their conjugates. Eberhard\, Ford and Green built upon the work of ma
 ny others and showed that\, as $n \\rightarrow \\infty$\, the probability 
 that $S_n$ is invariably generated by a random set of elements is bounded 
 away from zero if there are four random elements\, but goes to zero if we 
 pick three random elements. This result gives rise to a nice Monte Carlo a
 lgorithm for computing Galois groups of polynomials. We will extend this r
 esult for $S_n$ to the finite classical groups using the correspondence be
 tween classes of maximal tori of classical groups and conjugacy classes of
  their Weyl groups.
LOCATION:Seminar Room 1\, Newton Institute
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