HIGGS BUNDLES AND SYZ GEOMETRY

Using non-Abelian Hodge correspondence for parabolic Higgs bundles and surface group representations, we construct infinitely many non-congruent hyperbolic affine spheres modeled on a thrice-punctured sphere with monodromy in SL₃(Z). These give rise to non-isometric semi-flat Calabi–Yau metrics on special Lagrangian torus bundles over an open ball in R³ with a Y-vertex deleted, thereby answering a question raised by Loftin, Yau, and Zaslow in [32, 33].