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.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/node/6370