BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:On the Chebotarev invariant of a finite group - Gareth Tracey (Uni
 versity of Bath)
DTSTART:20200114T110000Z
DTEND:20200114T120000Z
UID:TALK136627@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Given a &#12\;nite group X\, a classical approach to proving t
 hat X is the Galois groupof a Galois extension K=Q can be described roughl
 y as follows: (1) prove that Gal(K=Q) iscontained in X by using known prop
 erties of the extension (for example\, the Galois group of anirreducible p
 olynomial f(x) 2 Z[x] of degree n embeds into the symmetric group Sym(n))\
 ; (2)try to prove that X = Gal(K=Q) by computing the Frobenius automorphis
 ms modulo successiveprimes\, which gives conjugacy classes in Gal(K=Q)\, a
 nd hence in X. If these conjugacy classescan only occur in the case Gal(K=
 Q) = X\, then we are done. The Chebotarev invariant of Xcan roughly be des
 cribed as the e&#14\;ciency of this algorithm".In this talk we will de&#12
 \;ne the Chebotarev invariant precisely\, and describe some new resultscon
 cerning its asymptotic behaviour.
LOCATION:Seminar Room 2\, Newton Institute
END:VEVENT
END:VCALENDAR