Abstract: In Riemannian geometry, collapse imposes strong geometricand topological restrictions on the

spaces on which it occurs. In the case of Alexandrov spaces, which generalize Riemannian manifolds with

a lower sectioanl curvature bound, collapse is fairly well understood in dimension three. In this talk I will

discuss the topology of sufficiently collapsed Alexandrov 3-spaces: when the space is irreducible, it is

modeled on one of the eight three-dimensional dimensional Thurston geometries, excluding the

hyperbolic one. This extends a result of Shioya and Yamaguchi, originally formulated for Riemannian

manifolds, to the Alexandrov setting. This is joint work with Luis Guijarro and Jesús Núñez-Zimbrón.