Séminaire de Physique Théorique

Self-Similar Quasicrystals and Hyperbolic Honeycombs

by Prof. Justin Kulp (Perimeter Institute, Waterloo & IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois-Marie, 35, route de Chartres 91440 Bures-sur-Yvette

Most people are familiar with periodic tessellations and lattices; from the patio floor at the reception building to their favourite spin systems. In this talk, I will discuss two less familiar families of tessellations and their possible connections to high energy physics, condensed matter physics, and mathematics: hyperbolic tessellations and quasicrystals. After introducing the basics of regular hyperbolic lattices, I will survey constructions and surprising properties of quasicrystals (like the Penrose tiling), including their classically forbidden symmetries, long-range order, and self-similar structure. Inspired by the AdS/CFT correspondence, I will describe a mathematical relationship between hyperbolic lattices in (D+1)-dimensions and quasicrystals in D-dimensions, as well as the resolution of a conjecture by Bill Thurston. Based on work to appear with Latham Boyle.


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Organized by

Slava Rychkov & Ryan Thorngren