Assaf Naor: Coarse (non)Universality of Alexandrov Spaces

We will show that there exists a metric space that does not
admit a coarse embedding into any Alexandrov space of global
nonpositive curvature, thus answering a question of Gromov (1993). In
contrast, any metric space embeds coarsely into an Alexandrov space of
nonnegative curvature. Based on joint works with Andoni and Neiman,
and Eskenazis and Mendel.