3 problems

Let $n$ be an integer greater than $8$, and consider primitive $n$-squared origamis in $\mathcal{H}(4)$, with $\mathcal{H}^{\mathrm{odd}}(4)$ denoting the odd component and…

Let $p$ be a prime, and let … be a Markoff surface over $\mathbb{F}_p$. Call a level $k$ generic when it contains no orbits associated with $A_4$, $S_4$, or $A_5$. Let…

Let $R$ be a discrete valuation ring with residue field of order $q$, let $M$ be the finite abelian group associated with a partition $\lambda$, and let $G$ act on $M\times M$ as i…