8 problems

Let $M_Fcsubset\mathbb T^3$ be a connected smooth two-manifold homologous to zero, and let a magnetic field determine trajectories on it. For a smooth one-parameter family…

In a periodic energy surface, let the level-set trajectories induced by a magnetic field include strongly chaotic trajectories, meaning trajectories whose lifts to the plane have n…

Let $B(x)\ge 0$ be a magnetic field with flux … which may be infinite, and let $H$ denote the corresponding Pauli operator. Miller's conjecture. The dimension of its kernel should…

One-dimensional reduction conjecture. Under these assumptions,

Nonaccumulation criterion. There is no accumulation of complex eigenvalues of $P_3(b,V)$ near zero if and only if $\Re(V)>0$.

Let $\lambda_0(\alpha)$ be the ground state energy of the operator defined in the paper, and let $\hat{\nu}$ be its minimum value. A minimizer is a point…

Let $B\in C(\mathbb R^2)$ be a continuous magnetic field, and let $\mathcal E_B$ denote the energy space associated with $B$. The notation $B=\operatorname{curl} A'$ means that the…

Let $H^h$ be the operator acting in $L^2(M)$, let $\lambda_0(H^h)$ denote the bottom of its spectrum, let $k$ be the order of vanishing of the magnetic field under the current assu…