BCFG Hitchin integrable systems via orbifoldings

An intriguing relationship between Hitchin integrable systems and Calabi--Yau integrable systems, both associated to any complex ADE Lie group of adjoint type, was discovered by Diaconescu, Donagi and Pantev in 2006. For each such ADE Lie group, the construction centers around a family of corresponding quasi-projective Calabi--Yau threefolds. In his 2016 thesis, Beck generalized this construction to include the non-simply laced complex simple Lie groups, whose Dynkin diagrams are obtained from some of the ADE Dynkin diagrams by "folding''. In this talk, we report on recent joint work with Florian Beck and Ron Donagi, where in the above-mentioned correspondence between integrable systems, we relate the folding procedure to orbifoldings.