Crystallography of hyperbolic lattices: from children's drawings to Fuchsian groups

Speaker: Igor Boettcher

Date: Wed, Mar 17, 2021

Location: Zoom, PIMS, University of Saskachewan

Conference: quanTA CRG Seminar

Subject: Mathematics, Topology, Physics, Condensed Matter and Statistical Mechanics

Class: Scientific

CRG: Quantum Topology and its Applications (2020-2023)

Abstract:

yperbolic Lattices are tessellations of the hyperbolic plane
using, for instance, heptagons or octagons. They are relevant for quantum
error correcting codes and experimental simulations of quantum physics in
curved space. Underneath their perplexing beauty lies a hidden and,
perhaps, unexpected periodicity that allows us to identify the unit cell
and Bravais lattice for a given hyperbolic lattice. This paves the way for
applying powerful concepts from solid state physics and, potentially,
finding a generalization of Bloch's theorem to hyperbolic lattices. In my
talk, I will explain some of the mathematics underlying this hyperbolic
crystallography.

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