Samantha Pilgrim

Asymptotic Invariants and Hurewicz-type Theorems

A Hurewicz-type theorem for a dimension theory says roughly that if f is a morphism from X to Y, the dimension of X should be at most the dimension of Y plus the largest dimension of a "fibre" of f (speaking loosely). I will give an introduction to the generalized asymptotic invariants first introduced by David Hume, John M. Mackay, and Romain Tessera, beginning with Gromov's asymptotic dimension. Then I will discuss an approach for proving a Hurewicz-type theorem in this greater level of generality (joint work with David Hume). Depending on time, we might also discuss some applications to coarse geometry and dynamics.