Operator Algebra Seminar

Speaker:  Alain Valette (Université de Neuchâtel)

Title: Expanders and box spaces

Abstract : Expanders, especially those coming from box spaces of residually finite groups, have been used to test various forms of the coarse Baum-Connes conjecture. The first construction of a pair of expanders, one not coarsely embedding in the other, was provided by Mendel and Naor in 2012. This was extended by Hume in 2014 who constructed a continuum of expanders with unbounded girth, pairwise not coarsely equivalent. In joint work with A. Khukhro, we construct a continuum of expanders with geometric property (T) of Willett-Yu, as box spaces of SL(3,Z). We also show that, for m>n≥2, box spaces of SL(m,Z) are not coarsely equivalent to box spaces of SL(n,Z).