11:45 - 13:00 Lunch (meet at the atrium on the 1st floor of the Alan Turing Building)
13:00 - 14:00 Andrew Mitchell (Loughborough)
14:00 - 15:00 Sigrid Grepstad (Norwegian University of Science and Technology)
15:00 - 15:30 Refreshments
15:30 - 16:30 Mike Whittaker (Glasgow)
16:30 - 17:30 Bryn Davies (Warwick)
Pizza and drinks. There may be bowling(!)
Bryn Davies Floquet-Bloch methods for designing quasiperiodic acoustic metamaterials
Quasiperiodic metamaterials hold significant potential to unlock novel wave phenomena by exploiting fractal spectra to achieve exotic new topologies and unlock very broadband effects. However, many of the conventional methods for designing metamaterials rely on geometric periodicity. We present analyses of methods to approximate the spectra of differential operators on quasiperiodic domains: the superspace and supercell methods. These both rely on approximating the quasicrystal by a periodic geometry, such that Floquet-Bloch theory can be applied. We will show how these methods facilitate the systematic design of novel quasiperiodic metamaterials, such as topological (symmetry-induced) waveguides and graded metamaterials (with rainbow effects).
Sigrid Grepstad Bounded distance equivalent cut-and-project sets and equidecomposability
In this talk, we study bounded distance equivalence of cut-and-project sets in R^n constructed from a fixed lattice in R^n \times R^m, but using different window sets W and W' in R^m. In a 2025 IMRN paper, I claimed that, under mild regularity assumptions on the windows, two such cut-and-project sets are bounded distance equivalent if and only if the windows W and W' are equidecomposable in a certain sense. Unfortunately, the published proof contains an error. A corrected argument, of a rather different nature, is provided in https://arxiv.org/abs/2511.21148. I will briefly outline the corrected proof and clarify how the original error affects the remaining claims made in the IMRN paper.
The talk is based on joint work with Mark Etkind, Mihalis Kolountzakis and Nir Lev.
Andrew Mitchell Staggered substitutions
Sequences generated by substitutions provide the prototypical examples of mathematical quasicrystals and their dynamical properties are largely well understood. Staggered substitutions are a variation of substitutions where one substitution is applied at even positions and a possibly different substitution is applied at odd positions. In contrast to classical substitutions, there is still little known about sequences generated by staggered substitutions. Perhaps most notably, the Kolakoski sequence (OEIS A000002) can be generated by a staggered substitution, and its conjectured properties form some of the most pertinent open questions in symbolic dynamics.
In this talk, I will provide an introduction to staggered substitutions and highlight the main intricacies that arise in their study. I will also discuss some recent progress towards understanding the structure of some examples.
Mike Whittaker Self-similar actions on graphs and their limit spaces.
Self-similar actions on graphs extend the usual notion of self-similar groups. Exel and Pardo realised that a construction due to Katsura gives rise to self-similar actions on graphs. The construction is defined from two integer matrices and defines odometer type actions on edges of the graph. Nekrashevych and collaborators proved that the limit spaces of self-similar groups give generalised Julia sets with canonical dynamics. I'll show that the limit spaces of Katsura-Exel-Pardo actions often embed in the plane and provide some insights into why these objects are interesting from a dynamical perspective. This is joint work with Jeremy Hume.