11 problems

Sharp anticoncentration conjecture. For every tree $T$,

Lee's conjecture. For every tree $T$,

Let $d_0,c>0$ be universal constants. For every integer $d\geq d_0$, let $G$ be a connected $n$-vertex graph with minimum degree at least $d$, and let $\mathcal{T}$ be a uniformly…

Let $\varepsilon>0$ be real. There is a constant $d_{\varepsilon}>0$ such that for every integer $d\geq d_{\varepsilon}$, every connected $n$-vertex $d$-regular graph $G$, and a un…

Let $M_n^{sym}$ be a symmetric random matrix whose entries are independent Rademacher variables. Vu's distinct singular values conjecture. With probability $1-o(1)$, all the singul…

Let $0\le d<r$ and $q$ be integers. Let $\mathcal{Z}\subseteq\mathbb{R}^{r}$ be an algebraic variety of dimension $d$ and degree at most $q$. Let…

Anticoncentration conjecture.

Hypergraph logarithm-free inducibility bound conjecture. For any $r,k$ and any $0\le\ell\le\binom{k}{r}$, we have

Logarithm-free inducibility bound conjecture. For all $k$ and all $0\le\ell\le\binom{k}{2}$, we have

Alon–Hefetz–Krivelevich–Tyomkyn's superlinear sparsity conjecture. For all $k,\ell$ satisfying

Alon–Hefetz–Krivelevich–Tyomkyn's 1/e conjecture. For all $0<\ell<\binom{k}{2}$ we have