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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

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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.