4 problems

Doney's conjecture. 1. If $\sigma^2>0$, then

Let $f:M\rightarrow B$ be a generic special Lagrangian fibration of an almost Calabi–Yau $3$-fold, including fibres with singularities, where generic' has the meaning specified in…

Existence conjecture for $C_{k,r}$. There exists an integer $m=m(r)$ such that, for every finite field $\mathbb{F}_q$ with $q>m$ and characteristic not dividing $r$, there is some…

Let $S_{n+1}$ be the symmetric group, let ${\mathbf W}_n$ be the set of words, and let $\operatorname{inv}(\sigma)$ denote the inversion number of $\sigma$. For a nonidentity permu…