We investigate the arithmetic of algebraic curves on coarse moduli spaces for special linear rank two local systems on surfaces with fixed boundary traces. We prove a structure theorem for morphisms from the affine line into the moduli space. We show that the set of integral points on any nondegenerate algebraic curve on the moduli space can be effectively determined.
"Arithmetic of curves on moduli of local systems." Algebra Number Theory 14 (10) 2575 - 2605, 2020. https://doi.org/10.2140/ant.2020.14.2575