### Asymptotic dimension for covers with controlled growth

Geometry and Topology Seminar

31st October 2023, 2:00 pm – 3:00 pm

Fry Building, 2.04

The "asymptotic dimension" of a metric space is an invariant introduced

by Gromov as a large-scale analogue of topological dimension, where one

covers the space by uniformly bounded sets with controlled overlap. It

has many applications, one of which is as an obstruction to coarse

embeddings between spaces. I'll discuss recent work with Hume and

Tessera where we study analogous invariants where the covers are allowed

to be unbounded, but to grow slowly. This allowed us to show, for

example, that there is no coarse embedding of the hyperbolic plane into

the product of a regular tree and any Euclidean space, answering a

question of Benjamini-Schramm-Timar.

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