4 problems

Let two interval exchange systems be isogenous, and suppose one is minimal and self-induced. Then the other is also minimal and self-induced. Associate to such systems their transl…

On the double-hendecagon translation surface, a direction is called hyperbolic or parabolic according to the corresponding type for the surface's Veech group, and the trace field i…

Let $T$ be one of the algorithms considered in the paper, and let $F_2$ be the invariant trace field of the commensurability class of its associated group $\Gamma_T$. The height-de…

Finite-orbit conjecture. For every surface $L_{D,\epsilon}$ and every fixed number $N$, the set $\mathcal{P}_N$ decomposes into a finite number of…