On the hyperbolic Bloch transform

Ákos Nagy, BEIT Canada

Motivated by recent theoretical and experimental developments in the physics of hyperbolic crystals, I will introduce the noncommutative Bloch transform for Fuchsian groups which I will call the hyperbolic Bloch transform (HBT). The HBT transforms wave functions on the hyperbolic plane to sections of irreducible, flat, Hermitian vector bundles over the orbit space and transforms the hyperbolic Laplacian into the covariant Laplacian. I will prove that the HBT is injective and “asymptotically unitary”. If time permits, I will talk about potential applications to hyperbolic band theory. This is a joint work with Steve Rayan (arXiv:2208.02749).

MC 5417