6 problems

Discretized sticky Kakeya conjecture. For every $\varepsilon>0$ there exist $\eta=\eta_{n,\mathrm{rest}}(\varepsilon)>0$ and $\delta_0=\delta_{0,n,\mathrm{rest}}(\varepsilon)>0$ su…

Freedman–Headrick conjecture. The maximal flow and minimal cut on $(V,E)$ converge as

Let ${\cal A}$ be a set of $d\times d$ matrices, let $r$ be the maximal spectral radius of the matrices, let $\varepsilon$ be the prescribed accuracy, and let $K(r,\varepsilon)$ de…

The paper considers polynomial or rational vector fields and birational discretizations, meaning discretization methods whose update map and inverse are explicit. Birational discre…

Let $x_i$ be an original spike location for a non-dyadic measure, and consider the neighboring grid points relevant to the discrete minimal-norm certificate. Immediate-neighbor con…

Consider a non-dyadic measure and a sufficiently fine grid, in a regime where there is at most one pair of spikes at consecutive grid points in the neighborhood of each original sp…