7 problems

Sharpness conjecture. The upper bound is an equality:

HEALPix intersection conjecture. The maximum number of intersected pixels is

Let $n\in\mathds{Z}^+$, and consider the point configuration called Polar Coordinates with parameter $n$. For a direction on the sphere, let the directed Discrepancy be the discrep…

Bourgain–Sarnak–Rudnick-type conjecture. For every $\epsilon>0$,

Let $D(\omega_N)$ denote the spherical cap discrepancy of a sequence of configurations $\{\omega_N\}_{N=2}^{\infty}\subset\mathbb{S}^2$. Call the sequence well-separated when its p…

Let $d$ be a positive integer and consider unit vectors in $\mathbb C^d$. A set of vectors is equiangular when there is a constant $\alpha$ such that the relevant pairwise inner pr…

Let $Y_0,Y_1,\ldots$ be independent uniformly distributed random variables on the unit square, let $\boldsymbol{\Phi}$ be the area-preserving Lambert map from the square to…