# Magnus Goffeng: The dynamics and (noncommutative) geometry of Smale spaces

**Time: **
Wed 2019-04-24 15.30 - 16.30

**Location: **
Room 32, building 5, Kräftriket, Department of Mathematics, Stockholm University ￼

**Participating: **
Magnus Goffeng, Chalmers

Abstract:

In this talk we will discuss Smale spaces, their associated C*-algebras and a way of introducing a noncommutative geometry capturing their dynamics. A Smale space is a type of hyperbolic dynamical systems that generalizes axiom A diffeomorphisms, and carries a coordinate system locally decomposing the space into stable and unstable directions. They were axiomatized by Ruelle and studied further by Putnam. It was recently proven that the associated C*-algebras fit into Elliott’s classification program. If the stable sets are totally disconnected, one of the associated C*-algebras admit a Cuntz-Pimsner model on which we can do noncommutative geometry. Joint work with Robin Deeley, Bram Mesland, Michael Whittaker and Allan Yashinski.