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The Penrose tiling, self-similar quasicrystals, and fundamental physics


Event description

I will begin with the Penrose tiling -- the most famous example of a self-similar quasi-periodic pattern. In addition to its beauty and mathematical interest, this pattern has a classic physical application to exotic materials called quasicrystals. But, in this talk, I will explain two new physical contexts in which such patterns appear:

(1) First, I will show that a regular tiling of hyperbolic space naturally decomposes into a sequence of self-similar quasicrystalline slices, with each slice related to the next by an invertible local "inflation/deflation" rule, so that the whole tiling may be reconstructed from a single slice. (In particular, the self-dual tiling of hyperbolic space by icosahedra essentially breaks into a sequence of Penrose tilings, as conjectured by Thurston.) I will explain how this relates to recent efforts to formulate discrete versions of the holographic principle.

(2) Second, I will show how the symmetries of the remarkable lattice II_{9,1} (the even self-dual lattice in 9+1 dimensional Minkowski space) define a 3+1 dimensional quasicrystal living inside it. I will explain some (speculative) reasons to wonder if such a quasicrystal might provide a relevant model for our own 3+1 dimensional spacetime.

The Penrose tiling, self-similar quasicrystals, and fundamental physics


Higgs Centre Seminar Room, JCMB (Find us on campus maps)
The Higgs Centre for Theoretical Physics
School of Physics and Astronomy
James Clerk Maxwell Building, 4305
Peter Guthrie Tait Road

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