Functional Analysis Seminar

Guentner, Willet and Yu defined a notion of dynamic asymptotic dimension for an étale groupoid that can be used to bound the nuclear dimension of its groupoid C*-algebra.  To have finite dynamic asymptotic dimension, the isotropy subgroups of the groupoid must be locally finite.  I will discuss 1) how to use similar ideas to bound the nuclear dimension of the C*-algebra of a groupoid with `large' isotropy subgroups and 2) the limitations of that approach. In an application to the C*-algebra of a directed graph,  if the C*-algebra is stably finite, then its nuclear dimension is at most 1.  This is joint work with Dana Williams. 

The landmark completion of the Elliott classification program for unital separable simple nuclear C*-algebras saw three regularity properties rise to prominence: Z-stability, a C*-algebraic analogue of von Neumann algebras' McDuffness; finite nuclear dimension, an operator algebraic version of having finite Lebesgue dimension; and strict comparison, a generalization of tracial comparison in II_1 factors. Given their relevance to classification, most of the investigations into their interplay have focused on the simple nuclear case.

 The purpose of this talk is to advertise the general study of these properties and discuss their applications both within and outside operator algebras. Concretely, I will explain how characterizing when certain twisted group C*-algebras are Z-stable can provide new partial solutions to a well-known problem in generalized time-frequency analysis; this is joint work with U. Enstad. If time allows, I will also briefly discuss how a different incarnation of tracial comparison (finite radius of comparison) for non-commutative tori relates to the existence of smooth Gabor frames; this last part is joint work with U. Enstad and also H. Thiel.

to follow

to follow

to follow

to follow

to follow

to follow

to follow