I will start by surveying Margulis' Super-Rigidity and Zimmer's cocyle Super-Rigidity.
I will then explain a method developed with Alex Furman, which allows to prove various extensions of these theorems.
In the last part of the talk I will focus on some applications to groups which act on affine buildings.
I will sketch some open problems regarding such groups, related to the Zimmer conjecture.
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