  We construct infinitely many non-isotrivial families of abelian varieties
over given four punctured projective lines. These families lead to algebraic
solutions of Painleve VI equation. Finally, based on a recent paper by
Lin-Sheng-Wang, we prove a complete characterization for the locus of motivic
Higgs bundles in the moduli space as fixed points of an ``additive'' self-map.
This is a note based on the lecture given by the second named author on 04 Nov.
2022 at Tsinghua University.
