Abstract:
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.
