10 problems

Mundici's conjecture. The quantity $C(Q)$ is less than $3$ for all $Q\geq 2$.

For $n\in\mathbb{N}$, let $N_n$ be a Poisson random variable with parameter $n$, and let $\mathcal{P}_{N_n,d}^{\bbbeta}$ and $\mathcal{P}_{n,d}^{\bbbeta}$ denote the corresponding…

Let $\bbbeta=(\beta_1,\ldots,\beta_m)$ be the block-parameter vector for the block-beta random polytope $\mathcal{P}_{n,d}^{\bbbeta}$. Negative-parameter extension conjecture. The…

Let $m\in\mathbb{N}$. For $i\in\\{1,\dotsc,m\\}$, let $K_i\subset \mathbb{R}^{d_i}$ be a convex body whose boundary is twice differentiable with positive Gaussian curvature everywh…

Let $d$ and $\tau$ be the small distance and time parameters used in the transition estimates, and let $\Sigma^{\textrm{fwd}}$, $K_2^\mu$, $K^\mu$, $\varepsilon$, $C$,…

Let $A_n$ be a root system with positive roots $\Sigma^+$, Weyl group $W$, and positive Weyl chamber $C^+$. For a Weyl chamber $C$, let $\mathcal{Short}(C)\subset W$ be the set of…

Growth conjecture for primary Carmichael numbers. For sufficiently small $\varepsilon>0$,

Let $f_l$ be the random spherical harmonic and let $V$ be the vector field on $S^2$ considered above. Writing $DF_l$ for the derivative of the map $F_l=(f_l,Vf_l)$ and…

Let … so that $b_0=1$ and the coefficients $b_{\nu}$ are those of the reciprocal power series. Coefficient-decay conjecture. … Such an estimate would provide the better control of…

Growth conjecture for $\mathcal{P}_r$. For each $r$, there is a number $\delta_r>0$ such that