Nonlinear descent on moduli of local systems

We discuss the Diophantine geometry of moduli spaces for special linear rank two local systems on topological surfaces with fixed boundary traces. We show that they form a rich family of log Calabi–Yau varieties, where a structure theorem for their integral points can be established using mapping class group dynamics. This generalizes a classical Diophantine work of Markoff (1880). Related analysis also yields new results on the arithmetic of curves in these moduli spaces.