5 problems

Let $X_n$ denote the set of points where the behavior of the eigenfunctions corresponding to the $n$th band function is not covered by the known differentiability result, and let b…

The discussion concerns gyrotropic photonic crystals, whose bulk phases are classified in class A by integer-valued Chern numbers, including a first Chern number in two dimensions.…

Let $\nu^\pm_{l,\infty}$, with $l\in\mathbb{N}_0$, be the Bloch measures generated by a solution of the scattering problem, and let $J^\pm_{=0,l}$ denote the corresponding sets of…

A three-dimensional photonic crystal is a periodic structure whose electromagnetic spectrum may contain an omnidirectional band gap, meaning a frequency interval with no propagatin…

Sommerfeld–Bethe conjecture. In dimensions $d=2$ and $d=3$, the number of gaps is finite.