Pure Maths Colloquium: Regularity of aperiodic minimal subshifts
30 August 2017 16:00 in CM221
The theory of aperiodic order is a relatively young field of mathematics, which has attracted considerable attention in recent years. It has grown rapidly over the past three decades; on the one hand, due to the discovery of quasicrystals; and on the other hand, due to intrinsic mathematical interest in describing the very border between crystallinity and aperiodicity. While there is currently no axiomatic framework for aperiodic order, various types of order conditions have been and are still being studied.
At the turn of the century Durand and Lagarias & Pleasants established key order conditions to be studied. In this talk, we will discuss these order conditions, as well as generalisations and extensions thereof, for two classes of aperiodic dynamical systems: Sturmian subshifts and a new family of subshifts stemming from Grigorchuk's infinite 2-group. We will also show that (exact) Jarník sets naturally give rise to a classification of Sturmian subshifts in terms of such order conditions.
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