Inspired by some questions presented in a recent arXiv preprint(version v1) by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff,we analyze their conjecture that the ground state energy of the magneticDirichlet-to-Neumann operator tends to $+\infty$ as the magnetic fieldtends to $+\infty$. More precisely, we explore refined conjectures forgeneral domains in $\mathbb R^2$ or $ \mathbb R^3$ based on theprevious analysis in the case of the half-plane and the disk. Thispart is a work in collaboration with Ayman Kachmar and Fran\c{c}oisNicoleau. In connexion with old works on the magnetic Schr\"odingeroperator with J. Nourrigat, we will also discuss, if time permits,recent results by Zhongwei Shen.
