$F_2$ cohomology of arithmetic groups applied to discrete math, computer science and topology

Expander graphs have been a focus of interest in computer science in the last 40 years and in the
last 10 years also in pure math. In recent years a high dimensional theory of expanders is emerged.
A fundamental concept  there is the coboundry expander. Cohomology of arithmetic groups
( mainly with coefficients in in $F_2$) plays an important role in these developments. We will
present some applications to topology and computer science as well as some open problems.