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PRODID:UWA Whatson 2002
X-WR-CALNAME;VALUE=TEXT:What's On At UWA
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DTSTART:19700101T000000
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BEGIN:VEVENT
UID:P-20100719T075650Z-1235-24446@events.uwa.edu.au
DTSTART;TZID=/softwarestudio.org/Olson_20010626_2/Australia/Perth:20100721T110000
DTEND;TZID=/softwarestudio.org/Olson_20010626_2/Australia/Perth:20100727T134500
CLASS:PUBLIC
CREATED:20100719T075650Z
DESCRIPTION:Nick Gill (Bristol)\n\nwill continue his series of lectures on
growth in groups and graphs\n\nat the following times\n\nWednesday 21/7
at 11am\n\nFriday 23/7 at 11am\n\nand Tuesday 27/7 at 1pm\n\nAll seminars
will be held in MLR2\n\n\nI: Growth in soluble subgroups of GL_r(p)\n\nAbs
tract: We show how to reduce the study of exponential growth in soluble su
bgroups\nof GL_r(p) to the nilpotent setting. We make use of ideas based o
n the\nsum-product phenomenon\, as well as some machinery from linear alge
braic\ngroups. We will not assume any background from these areas.\n\nII:
An introduction to expanders\n\nAbstract: This is a background seminar pre
paring the way for Seminar III\, where we\nconnect results on growth in si
mple groups to the explicit construction of\nfamilies of expanders. In thi
s seminar we will define what we mean by a\nfamily of expanders\, stating
(and sometimes even proving!!) background\nresults that will be important
later.\n\nWe will also try to explain why expanders are of such interest t
o so many\ndifferent groups of people.\n\nIII: Using growth results to exp
licitly construct expanders\n\nAbstract: We outline the method of Bourgain
and Gamburd. They were the first to use\nresults concerning growth in sim
ple groups to explicitly construct\nexpander graphs. Let S be a set in SL_
2(Z) and define S_p to be the\nnatural projection of S modulo p. Now let G
_p be the Cayley graph of\nSL_2(F_p) with respect to the set S_p. Bourgain
and Gamburd give precise\nresults as to when the set of graphs {G_p : p a
prime} forms a family of\nexpanders. They make crucial use of the result
of Helfgott (encountered in\nan earlier seminar) which states that "all ge
nerating sets in SL_2(p)\ngrow".\n\n\nAll welcome\n\nSpeakers: Nick Gill
DTSTAMP:20100719T075650Z
LAST-MODIFIED:20100908T044232Z
LOCATION:Maths Lecture Room 2
ORGANIZER;CN=Michael Giudici:MAILTO:giudici@maths.uwa.edu.au
SEQUENCE:3
SUMMARY:Lectures on Growth in Groups and Graphs Part II
URL:https://events.uwa.edu.au/event/20100719T075650Z-1235-24446@events.uwa.
edu.au/whatson/CMSC
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