13 problems

Let $f$ be a nonuniformly expanding map. Perturbation-persistence conjecture. Sufficiently small perturbations of $f$ have positive probability of also being nonuniformly expanding…

Let $f(x_1,\ldots,x_n)$ be a homogeneous polynomial and let $\mathcal D$ be as in the preceding conjecture. Thus condition $(A)$ means that $f$ can be written as … where each $f_m$…

Let ${{\mathscr M}}_{\epsilon}$ be a physical spacetime, let ${{\mathscr M}}$ be its background spacetime, and let $h_{ab}$ be a perturbative metric tensor pulled back from…

Abelian Higgs correlator theorem. The correlator may be obtained by applying $\mathcal{T}_{\mathrm{cont}}$ to

Let $\mathcal{T}$ be an equiangular tight frame decomposable tensor, meaning a symmetric tensor admitting a decomposition into powers of vectors from an equiangular tight frame. Th…

Real-part spectral-symbol conjecture. Is it true that

Small trace-norm perturbation conjecture. Then

Let $T$ be the Toeplitz matrix and let $A_{jj}$ denote the matrix with its $(j,j)$ entry selected. Consider the rank-one deformation … Let the first-order perturbation correction b…

Higher-order gauge-transformation conjecture. There exists a vector field $\hat\sigma_{(n)}^a$ such that

Let $\mathcal H$ be a Hilbert space, let $\mathcal B(\mathcal H)$ denote the bounded operators on $\mathcal H$, and let $d(M,N)$ be the Hausdorff distance between the unit balls of…

Decomposition conjecture. There exist a tensor field ${\cal H}_{ab}$ and a vector field $X^a$ such that

Let $M$ be a Riemannian manifold, and let $P_1$ and $P_2$ be subcritical elliptic operators of the form specified in the paper. Two heat kernels are equivalent when they are compar…

Let $\epsilon$ and $\delta$ be the perturbation parameters, and let $\mathcal{H}_{nm}$ denote the Hamiltonian contribution of bidegree $(n,m)$ in the grading with respect to…