Sanaz
Pooya
University of Potsdam
What is Kazhdan Property (T)?
Abstract.
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.