Asymptotic cones of finitely presented groups

Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) is at least 2, and let $\Gamma$ be a uniform lattice in G. (a) If $CH$ holds, then $\Gamma$ has a unique asymptotic cone up to homeomorphism. (b) If $CH$ fails, then $\Gamma$ has $2^{2^{\omega}}$ asymptotic cones up to homeomorphism.Comment: To appear in Advances in Mathematic

Logic and operator algebras

The most recent wave of applications of logic to operator algebras is a young and rapidly developing field. This is a snapshot of the current state of the art.Comment: A minor chang