The discovery of the Penrose tiling (and other self-similar quasiperiodic tilings) in the 1970s sparked research into the remarkable mathematical properties of quasiperiodic structures, revealing connections to Fourier theory, number theory, and even pure logic. Soon after, these tilings found a classic application in physics as models for “quasicrystals”, new materials first discovered in the lab in 1984 by Daniel Schectman (Nobel Prize, 2011). Experimental and theoretical studies of this classic (materials science) application continues to be an active research area to this day.
However, novel quasicrystal-related ideas have also recently emerged in a number of quite different areas in high-energy, condensed matter, and mathematical physics, including e.g.: quasicrsytalline topological phases (i.e. novel topological phases of matter protected by quasicrsytalline order), quasicrsytalline orbiforlds (novel string compactificiations with properties of both theoretical and mathematical interests), quantum error correcting codes (where it was recently realised that quasiperiodic tilings are blueprints for such codes), and discrete holography (since tessellations of (d+1)-dimensional hyperbolic space naturally decompose into d-dimensional quasicrystals). This, in turn, relates to recent work on the physics of discrete/lattice models in hyperbolic space.
This is the first workshop that aims to explore and build upon the connections between these novel directions in theoretical and mathematical physics.
