10 problems

Let $G_{\mathcal{O}}$ be a scalar two-point function on the Euclidean sphere satisfying the stated Euclidean assumptions: it is regular at non-coincident points, $SO(d+2)$-invarian…

Let $M\subset\mathbb S^{n+1}_1$ be a spacelike, compact, star-shaped, and $k$-convex hypersurface. For $1\leq k\leq n$, let $\mathcal A_k$ denote the quermassintegral-type quantity…

Let $d$ be the spacetime dimension, let $uinmathbb{C}$ satisfy … and let $G_0^{\mathrm{sym}}$, $G_0^{\mathrm{sym},A}$, $G^{\mathrm{PJ}}$, and $G^{\mathrm{PJ},A}$ be the invariant…

Let $\mathcal{O}(Y)$ be a scalar local operator in a unitary quantum field theory in de Sitter space, acting on the Bunch–Davies vacuum. Denote by $\mathcal{V}_{p,0}$ the exception…

The string algebra is the Clifford algebra of the Hilbert space associated with the binary tree representing the design, while the algebra of observables for de Sitter space is a v…

Quermassintegral inequalities conjecture. There hold

Normalisation-factor conjecture. For every rank $r\geq 1$ and every possible type $B$ of STSSH on $S^N$, the normalisation factors are given by

Rigidity conjecture. The space $\mathcal{R}_{\rm op}(V_\nu,\Gamma_\nu)$ contains only trivial operators.

Consider the massless minimally coupled Klein–Gordon field on de Sitter spacetime, and require invariance under the de Sitter boost isometries considered in the paper. De Sitter bo…

Vanishing-norm conjecture. For $\sigma=-p-2$ and $0\leq L\leq p-1$, the norm of the singular solution vanishes, just as the norm of the regular solution does: