# Operator theory and coarse geometry

### Jan Spakula (University of Southampton)

Friday 14th March, 2014 14:40-15:25 504 Joseph Black Building

#### Abstract

(Some) operator theorists study Fredholmness of certain operators on l^2(Z^n)using the so-called operator spectrum. John Roe, in 2004, explained that the operators of interest are really just elements of the Translation C*-algebra (also called the uniform Roe algebra) of Z^nZn, the C*-algebra encoding the large scale (or coarse) structure of Z^n. In this talk, I will explain how to further exploit the inherent connections to coarse geometry to generalise a recent result of Lindner and Siedel, which significantly simplifies the Fredholmness criterion (they refer to the problem they solve as "The big question on Limit Operators (on Z^n)")