| | | Dr Yotam Smilansky
~ Hyperbolic Multiscale Tilings and their Orbits ~
The third of talk of the day switched away from applications of the aperiodic to focus on tilings from the viewpoint of a pure mathematician. Yotam Smilansky has revisited the traditional methods of constructing aperiodic tilings, and explored a fundamental variation in which multiple distinct inflations at different scales are allowed. The basics of this were carefully explained and are to be found in his paper from 2021 with co-author Yaar Solomon, Multiscale Substitution Tilings. Building on that paper, Yotam has realised that his tilings have a natural existence in the hyperbolic plane, this in turn giving rise to some interesting Tiling Zeta Functions. The zeros of these exhibit curious behaviours in the complex plane that Yotam and Alon Nishry are currently investigating. It was generous of Yotam to share these unpublished thoughts with us, and I am certainly looking forward to the ideas being formally presented in a paper.
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