5 problems

Slow-dispersion conjecture. For every $\varepsilon>0$, there exists a choice of $\nu(t)$ such that the $L^1\to L^\infty$ decay rate is no faster than $t^{-\varepsilon}$; more preci…

Optimal-loss conjecture. Under these sharp exponential-sum bounds, the Strichartz estimates should hold with loss $1/6+\epsilon$ for every $\epsilon>0$ and arbitrary…

Weighted Lorentz dispersive estimates conjecture. For every $\alpha\ne0$ and $y\in\mathbb{R}^3$, one has

Let $H_{\alpha,y}$ be the Schrödinger operator with a point interaction of strength $\alpha$ at $y\in\mathbb{R}^3$, let $P_{ac}$ denote the projection onto its absolutely continuou…

Let $S(t)$ be the linear propagator, let $\mathscr{A}f(t)=\int_{\mathbb{R}}S(t-\tau)f(\tau)\,d\tau$ be the associated full-time integral operator, and let $\Box_k$ be the frequency…