# Jerusalem Mathematics Colloquium

Thursday, 11th March 2010, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Emmanuel Breuillard

(Universite Paris-Sud 11))

"Approximate groups and expanders"

** Abstract: **

The talk will be based on joint work with B. Green and T.
Tao. A few years ago the initial work of H. Helfgott, who introduced
such combinatorial ideas as the "sum-product phenomenon" in the study
of growth in finite simple groups, was spectacularly applied by
Bourgain and Gamburd to show that the Cayley graphs of the family of
groups SL(2,Z/pZ), p prime, could be turned into a family of expanders
for a wide range of possible choices of generating sets. These
striking developments motivated the need for a more systematic study
of "approximate groups", that is finite subsets of an ambient group
that are almost closed under multiplication in an appropriate sense.
In the talk I will present this notion due to T. Tao in some detail
and survey some recent progress by a variety of authors towards the
rough classification of approximate subgroups of various
non-commutative groups. I will also discuss resulting applications for
expanding properties of finite quotients of linear groups.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2009-10

Archive of talks