M. Whittaker (Glasgow)

will speak on

Fractal substitution tilings and applications to noncommutative geometry

Time: 4:15PM
Date: Tue 10th October 2017
Location: UCD Science North 125 [map]

Abstract: 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.

(This talk is part of the Analysis series.)

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