8 problems

Let $delta>0$, and let $rhob_{\delta}$ and $Vb_{\delta}$ be the density and velocity profiles defined by the sharp stratification and shear-flow setup. Let $mathcal C_{\delta}(k)$…

Consider the dispersion curve associated with the nonlocal nonlinear Schrödinger equation and the numerically computed soliton solutions. In the numerical experiment with…

Consider an elliptic periodic operator and vary its parameters, for example its periodic potential. Generic gap-edge non-degeneracy conjecture. For almost all such parameters, the…

Let $\Gamma$ be a $\mathbb{Z}^d$-periodic graph with one crossing edge per generator, let $H$ be a periodic self-adjoint operator acting on $\ell^2(\Gamma)$, and let…

Let $-elta+V$ be a Schrödinger operator on $\mathbb{R}^n$ with periodic potential, and let $\lambda_j(k)$ denote its band functions, with $k$ the quasimomentum. Spectral edges are…

Let $\pazocal{R}_3(\mathbf{k},t)$ denote the remainder arising from the third-cumulant correction in the perturbation expansion, and let $\tau\lambda^{-2}$ be kinetic time. Third-r…

Let $\Gamma$ be a graph, let $\Gamma_{\gamma_1,\ldots,\gamma_\beta}^{\mathrm{cut}}$ be its cut graph, and let $\lambda_n(\Gamma_{\mathrm{mag}}^{\alpha_1,\ldots,\alpha_\beta})$ deno…

S-matrix bootstrap conjecture. A unique S-matrix, primarily for strong interactions, can be determined from unitarity, Poincaré invariance, and the crossing property.