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PRODID:UWA Whatson 2002
X-WR-CALNAME;VALUE=TEXT:What's On At UWA
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BEGIN:VEVENT
UID:P-20100429T021410Z-1235-14982@events.uwa.edu.au
DTSTART;TZID=/softwarestudio.org/Olson_20010626_2/Australia/Perth:20100504T120000
DTEND;TZID=/softwarestudio.org/Olson_20010626_2/Australia/Perth:20100514T120000
CLASS:PUBLIC
CREATED:20100429T021410Z
DESCRIPTION:Nick Gill (University of Bristol) will be giving a series of t
hree talks on the topic of Growth in Groups and Graphs as follows:\n\n
* Tuesday 4 May\, 12 noon\, MLR2\, I: Sum-Product\n\n * Friday 7 May\,
11am\, MLR3\, II: Growth in Groups of Lie Type\n\n * Friday 14th May 11
am MLR3\, III: Escape\n\n\nThese are part of a UWA research collaboration
award funding visits to Perth by Nick Gill and Harald Helfgott. The aim of
the talks is to give the necessary background and introduction to researc
h in the area. Nick will give a further three talks later in the year. Ni
ck has prepared a page of supporting material at\nhttps://www.maths.bris.ac
.uk/~manpg/austlit.html\n\nThe titles and abstracts for the first three ta
lks are as follows.\n\nI: SUM-PRODUCT\nWe introduce the idea of growth in
groups\, before focussing on the abelian setting. We take a first look at
the sum-product principle\, with a brief foray into the connection between
sum-product results and incidence theorems.\n\nWe then focus on Helfgott
s restatement of the sum-product principle in terms of groups acting on
groups.\n\nII: GROWTH IN GROUPS OF LIE TYPE\nSince Helfgott first proved t
hat generating sets grow in SL_2(p) and SL_3(p)\, our understanding of
how to prove such results has developed a great deal. It is now possible
to prove that generating sets grow in any finite group of Lie type\; what
is more the most recent proofs are very direct they have no recourse to
the incidence theorems of Helfgotts original approach.\n\nWe give an ov
erview of this new approach\, which has come to be known as a pivotting
argument. There are five parts to this approach\, and we outline how the
se fit together.\n\nIII: ESCAPE\nThe principle of escape from subvarieti
es is the first step in proving growth in groups of Lie type. We give a
proof of this result\, and its most important application (for us) the
construction of regular semisimple elements.\n\nWe then examine other rela
ted ideas from algebraic geometry\, in particular the idea of non-singular
ity.\n\nSpeakers: Nick Gill
DTSTAMP:20100429T021410Z
LAST-MODIFIED:20100429T032840Z
LOCATION:Maths Lecture Room 2 and Maths Lecture Room 3
ORGANIZER;CN=Michael Giudici:MAILTO:giudici@maths.uwa.edu.au
SEQUENCE:2
SUMMARY:Lectures on Growth in Groups and Graphs
URL:https://events.uwa.edu.au/event/20100429T021410Z-1235-14982@events.uwa.
edu.au/whatson/CMSC
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