3 problems

Let $X_n$ be the translation surface obtained from the regular $n$-gon, and let $l_0$ be the length of a side of the $n$-gon. For $n\geq 10$ with $n\equiv 2\pmod 4$, and for closed…

Let $S(w,e)$ be a Veech surface that is a Prym eigenform in the minimal stratum in genus $3$. A point of a Veech surface is periodic if it has finite orbit under its affine automor…

Let $q>9$, let $\lambda_q=2\cos(\pi/q)$, let $\mathbb Q(\lambda_q)$ be the field generated by $\lambda_q$, and let $G_q$ be the corresponding Hecke group acting on the real project…