Higher-rank universal lattices and Steinberg groups over Z[t_1,…,t_m] can be viewed as generalizations of higher-rank algebraic lattices.
In this lecture, I will discuss results showing that these groups possess the fixed point property for all affine isometric actions on uniformly convex Banach spaces. This result provides a far-reaching extension of my earlier work on Banach property (T) for SL(n,Z) that was later generalized by de Laat and de la Salle for all higher rank algebraic lattices.
