Actions de groupes de Kazhdan sur le cercle

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On the dynamics of (left) orderable groups (2007, background): “), and the question of knowing whether some particular classes of groups can be ordered (higher rank lattices [35, 34, 42], groups with Kazhdan’s property (T) [10, 44], etc.”
GROUP ACTIONS ON 1-MANIFOLDS: A LIST OF VERY CONCRETE OPEN QUESTIONS (2017, background): “A concrete result on this concerns actions by diffeomorphisms: If a finitely-generated group of C3/2 circle diffeomorphisms satisfies property (T), then it is finite [101, 110] (see [26] for the piecewise-smooth case).”
Property (T) and rigidity for actions on Banach spaces (2005, methodology): “n group [Po2]; • Ergodic theory – rigidity results related to Orbit Equivalence [Po3],[Hj]; the Banach–Ruziewicz problem [M3],[Su]; • Smooth dynamics–local rigidity [FM1],[FM2]; actions on the circle [N1] (and [PS],[Rz]). It has also been an important tool in providing interesting (counter) examples”