Property (T) for groups graded by root systems

In this talk I will first outline a general method for proving property
(T), first introduced by Dymara and Januszkiewicz in the context of groups acting
on buildings and then extended to a purely algebraic setting. Then I will explain
how this method can be applied to the class of groups graded by root systems. In
particular, it follows that for any reduced irreducible classical root system of rank
at least 2 and a finitely generated commutative ring R with 1, the Steinberg group
St(R) and the elementary Chevalley group E(R) have property (T).
The talk will be primarily based on a joint work with Andrei Jaikin-Zapirain
and Martin Kassabov.