“The paper shows that almost proper varieties, as well as p-adic (weakly admissible) period domains in the sense of Rappoport-Zink belong to this class.”

“The paper determines the robust optimal growth rate, constructs a worst-case admissible model, and characterizes the robust growth-optimal strategy via a solution to a certain partial differential equation (PDE).”

“The paper shows that changing the gluing edge isomorphisms does not affect the quasi-isometry type of these groups.”

“If a reflexive sheaf $\mathcal{E}$ on a log terminal Kähler-Einstein variety $(X,ω)$ is slope stable with respect to a singular Kähler-Einstein metric $ω$, then $\mathcal{E}$ admits an $ω$-admissible Hermitian-Yang-Mills metric.”

“The consistent orderings are in one-to-one correspondence with the Jacobians associated with all field redefinitions of a set of canonical degrees of freedom. For each admissible operator ordering--or equivalently, each path-integral measure--we identify a definite, positive Hilbert-space inner product. All such prescriptions define the same quantum theory, in the sense that they lead to identical physical observables.”

“The paper proposes three axioms that formalize the minimal invariance and stability properties required of rank-based input normalization.”