SEMINAR: Lectures on Growth in Groups and Graphs Part II


Nick Gill (Bristol)
will continue his series of lectures on growth in groups and graphs
at the following times
Wednesday 21/7 at 11am
Friday 23/7 at 11am
and Tuesday 27/7 at 1pm
All seminars will be held in MLR2
I: Growth in soluble subgroups of GL_r(p)
Abstract: We show how to reduce the study of exponential growth in soluble subgroups
of GL_r(p) to the nilpotent setting. We make use of ideas based on the
sumproduct phenomenon, as well as some machinery from linear algebraic
groups. We will not assume any background from these areas.
II: An introduction to expanders
Abstract: This is a background seminar preparing the way for Seminar III, where we
connect results on growth in simple groups to the explicit construction of
families of expanders. In this seminar we will define what we mean by a
family of expanders, stating (and sometimes even proving!!) background
results that will be important later.
We will also try to explain why expanders are of such interest to so many
different groups of people.
III: Using growth results to explicitly construct expanders
Abstract: We outline the method of Bourgain and Gamburd. They were the first to use
results concerning growth in simple groups to explicitly construct
expander graphs. Let S be a set in SL_2(Z) and define S_p to be the
natural projection of S modulo p. Now let G_p be the Cayley graph of
SL_2(F_p) with respect to the set S_p. Bourgain and Gamburd give precise
results as to when the set of graphs {G_p : p a prime} forms a family of
expanders. They make crucial use of the result of Helfgott (encountered in
an earlier seminar) which states that "all generating sets in SL_2(p)
grow".
All welcome
Speaker(s) 
Nick Gill

Location 
Maths Lecture Room 2


Contact 
Michael Giudici
<[email protected]>

Start 
Wed, 21 Jul 2010 11:00

End 
Tue, 27 Jul 2010 13:45

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Wed, 08 Sep 2010 12:42

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