Abstract: 
Motivated by Connes' rigidity conjecture, S. Popa conjectured in 2005 that fundamental groups of any property ($T$) group factor must be trivial. In this talk I shall give new examples of Property ($T$) group factors with trivial fundamental group.

This talk is partially based on a joint work with Ionut Chifan, Krishnendu Khan and Cyril Houdayer.