11 problems

Let $M$ be a Riemannian manifold, let $E$ be a Hermitian vector bundle over $M$, and let $V$ be a potential satisfying Assumption A: $V=V_{+}+V_{-}$, with $V_{+}(x)8e0$ and…

Local regularity conjecture. Under these assumptions,

Let $(M,g)$ be an asymptotically static spacetime, possibly with general behaviour in the spatial directions, and let $\square_g$ denote its wave operator. Dereziński's conjecture.…

Let $M$ be a compact manifold and let $P$ be a symmetric differential operator on $M$. The principal symbol of $P$ defines a Hamiltonian flow on the cotangent bundle of $M$. Colin…

Hamilton-flow completeness conjecture. Completeness of the Hamilton flow implies essential self-adjointness for non-elliptic operators on closed manifolds.

The classical and quantum notions involved are completeness of the Hamilton flow associated with a real principal symbol and essential self-adjointness of the corresponding pseudod…

Classical–quantum completeness conjecture. The Hamiltonian flow of $p$ is complete if and only if $P$ is essentially self-adjoint.

Let $M$ be a sub-Riemannian manifold, let its equiregular region be the complement of the singular region of the sub-Riemannian structure, and let $\Delta_{\mathcal P}$ denote the…

Let $N$ be a smooth manifold equipped with a sub-Riemannian structure that is rank-varying or non-equiregular on an embedded hypersurface, and let $\Delta$ denote its Laplace-Beltr…

An almost-Riemannian structure (ARS) is a Riemannian metric that is singular on an embedded smooth hypersurface and smooth on its complement. Let $M$ be the nonsingular part of an…

Let a sub-Riemannian structure be rank-varying or not equiregular on a hypersurface, and let the singular set be the set where the structure has this rank variation or failure of e…