Algebry operatorów i ich zastosowania w fizyce

We discuss some results of a joint project with Brady Killough and Michael Whittaker. The goal of the project is to better understand the functorial properties of the homology theory for Smale spaces introduced by Ian Putnam. This homology theory is conjecturally linked to the K-theory of the C*-algebras associated to a Smale space.Inspired by Connes and Skandalis' notion of correspondences in KK-theory, we define correspondences in the setting of Smale spaces. The basic idea is to encode both types of functorial properties of Smale spaces (with respect to Putnam's homology theory) into a single object. The talk will be very much an introduction and will contain many examples (for the most part coming from the theory of shifts of finite type). No knowledge of Smale spaces or Putnam's homology theory are required for the talk.