5 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 $n$ be a positive integer, and let $\mathcal{A}_n(1,1)$ and $\mathcal{S}_n(1,1)$ denote the cardinalities of the orbits of primitive $n$-squared origamis in $\mathcal{H}(1,1)$…

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 $b_{m,n}$ denote the number of Borel orbits of the symmetric variety $SO_{2m+2n+1}/S(O_{2m} \times O_{2n+1})$. For fixed $n$, this number is a polynomial in $m$. Can–Uu{g}urlu'…

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…