A topological classification of canonical cut and project tilings


The event is taking part on the Thursday, Nov 22nd 2018 at 15:30
Location of Event: Alan Turing Room 306
This event is a: Public Seminar

Abstract: :Given an aperiodic tiling of the plane, we can assign to it the space of all tilings which are 'locally isomorphic' to the original. This tiling space has a natural translation action. The topology and dynamics of these tiling spaces then reveal properties of the original tiling and vice versa. In general, these spaces are almost never the 'nice'
spaces we expect to see in topology or geometry. I will speak about how one particular invariant of these spaces, the Cech cohomology, can fully classify large classes of these tilings. To do this, we need to prescribe a natural ordering on the cohomology groups which is in some way related to the densities of patches in the original tiling.

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External Speakers

Dan Rust (University of Bielefeld)