6 papers
Dynamical Perturbing and -algebra Lifting Problems
Samantha Pilgrim
Approximate morphisms have seen significant study across many areas of mathematics, for instance, in the theory of Absolute (Neighborhood) Retracts in topology, or of almost-commut…
Topological Rigidity of the Dynamic Asymptotic Dimension
Samantha Pilgrim
We show for a free action of a countable group on a finite-dimensional, compact metric space by homeomorphisms that the dynamic asymptotic dimension is either infinite or coinc…
A Hurewicz-type Theorem for the Dynamic Asymptotic Dimension with Applications to Coarse Geometry and Dynamics
Samantha Pilgrim
We prove a Hurewicz-type theorem for the dynamic asymptotic dimension originally introduced by Guentner, Willett, and Yu. Calculations of (or simply upper bounds on) this dimension…
Isometric Actions are Quasidiagonal
Samantha Pilgrim
We show every isometric action is quasidiagonal in a strong sense. This shows that reduced crossed products by such actions are quasidiagonal or MF whenever the reduced algebra of…
Isometric Actions and Finite Approximations
Samantha Pilgrim
We show that every isometric action on a Cantor set is conjugate to an inverse limit of actions on finite sets; and that every isometric action by a finitely generated amenable gro…
Dynamic Asymptotic Dimension of Translation Actions on Compact Lie Groups
Samantha Pilgrim
We develop a method to bound the dynamic asymptotic dimension of isometric group actions in terms of the asymptotic dimension of a space of graphs similar to…