Property (T), a rigidity property for groups, was introduced by Kazhdan in 1967. It is connected to the theory of expander graphs, which are sequences of graphs that are sparse and well connected at the same time. Notably, Margulis in 1973 exploited property (T) and constructed the first explicit example of an expander. While existence of expanders was known thanks to a probabilistic proof, an explicit construction was a highly non-trivial problem at the time. In this talk, I will define both property (T) and expander graphs. The example of special linear groups will exemplify Margulis' construction. In the end, I will briefly mention a higher dimensional analogue of property (T) that has attracted interest over the past decade.
