9 problems

Kahle–Newman conjecture. The distribution of the Sylow $p$-subgroup of $H_1(C_n)$ follows the Cohen–Lenstra distribution.

Kahle–Newman conjecture. For every finite abelian $p$-group $G$,

General support-pattern conjecture.

For each $n$, let $\Sigma_n=(\sigma_{n,1},\ldots,\sigma_{n,n})$, where each $\sigma_{n,j}$ is a subset of $[n]=\{1,2,\ldots,n\}$. Let $X_n\in\operatorname{M}_n(\mathbb{Z}_p)$ be Ha…

Cohen–Lenstra conjecture for $p=3$. $\operatorname{Conj}^{+}(3,\alpha)$ and $\operatorname{Conj}^{-}(3,\alpha)$ are true for every positive integer $\alpha$.

Let $\mathrm{C}_3$ be a cyclic group of order $3$, and consider Galois number fields with Galois group isomorphic to $\mathrm{C}_3$ and class number $7$. The two non-trivial…

For $k\in\mathbb{N}$, let $\lambda_k$ be the probability distribution on finite abelian groups that assigns probability proportional to … to each finite abelian group $G$. Let…

Let $G$ be an Erdős–Rényi random graph, let $\Gamma(G)$ be its sandpile group, and let $\langle\cdot,\cdot\rangle_G$ denote its canonical symmetric perfect bilinear pairing. The pa…

Let $G$ be a finitely generated pro-$p$ group. Let $\operatorname{Freq}(G)$ denote its limiting frequency among imaginary quadratic fields, and let $\operatorname{Meas}(G)$ denote…