BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.bham.ac.uk//v3//EN
BEGIN:VEVENT
CATEGORIES:Groups St Andrews 2017
SUMMARY:The diameter of the symmetric group: ideas and too
ls - Harald Helfgott\, University of Göttingen
DTSTART:20170812T123000Z
DTEND:20170812T133000Z
UID:TALK2732AT
URL:/talk/index/2732
DESCRIPTION:Given a finite group _G_ and a set _A_ of generato
rs\, the diameter diam(Γ(*G*\,*A*)) of t
he Cayley graph Γ(*G*\,*A*) is the small
est ℓ such that every element of _G_ can be expres
sed as a word of length at most ℓ in _A_ ∪ *A*^{-1}. We are concerned with bounding dia
m(*G*) := max_{A} diam(Γ(*G<
/i>\,**A*)).\n\nIt has long been conjectured t
hat the diameter of the symmetric group of degree
_n_ is polynomially bounded in _n_. In 2011\, Helf
gott and Seress gave a quasipolynomial bound (exp(
(log *n*)^{(4+ε)})). We will discuss
a recent\, much simplified version of the proof\,
emphasising the links in commons with previous wor
k on growth in linear algebraic groups.
LOCATION:Poynting Physics\, Large Lecture Theatre
CONTACT:David Craven
END:VEVENT
END:VCALENDAR