**Uri Bader**

Weizmann Institute of Science, Israel

January 5, 2017

**On an ergodic theoretical method in the study of linear groups.**:
Ergodic theory is a valuable tool in the study of linear groups, notable examples being the celebrated rigidity results of Mostow and Margulis. In a joint work with Alex Furman we clarified the foundational basis beyond this phenomenon, studying the category of ``algebraic representation of ergodic actions''. This approach enables us to give new proofs of the above-mentioned theorems, as well as to obtain some new results. Recently, using this approach, in a joint work with Caprace and Lecureux we managed to prove the conjectural nonlinearity of certain class of groups acting on buildings. In my talk I will survey this circle of ideas.