Self-Similar Quasicrystals and Hyperbolic Honeycombs


Kulp, J. (2023). Self-Similar Quasicrystals and Hyperbolic Honeycombs. Perimeter Institute. https://pirsa.org/23010112


Kulp, Justin. Self-Similar Quasicrystals and Hyperbolic Honeycombs. Perimeter Institute, Jan. 27, 2023, https://pirsa.org/23010112


          @misc{ pirsa_23010112,
            doi = {10.48660/23010112},
            url = {https://pirsa.org/23010112},
            author = {Kulp, Justin},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Self-Similar Quasicrystals and Hyperbolic Honeycombs},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {jan},
            note = {PIRSA:23010112 see, \url{https://pirsa.org}}

Justin Kulp Perimeter Institute


Most people are familiar with periodic tessellations and lattices; from the floor in the PI Bistro to their favourite spin systems. In this talk, I will discuss two less familiar families of tessellations and their applications 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.

Zoom Link: https://pitp.zoom.us/j/91876287518?pwd=NGNLOXZHa1h1cmdnMzJxQzVMVFJJdz09