Pure Maths Colloquium: Fractal substitution tilings and applications to noncommutative geometry
6 February 2017 16:00 in CM221
Starting with a substitution tiling, such as the Penrose tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles typically have fractal boundary. As an application of fractal tilings, we construct an odd spectral triple on a C*-algebra associated with an aperiodic substitution tiling. Even though spectral triples on substitution tilings have been extremely well studied in the last 25 years, our construction produces the first truly noncommutative spectral triple associated with a tiling. My work on fractal substitution tilings is joint with Natalie Frank and Sam Webster, and my work on spectral triples is joint with Michael Mampusti.
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