Some topics in Kobayashi–Hitchin correspondences

Recently, we studied the Kobayashi–Hitchin correspondences for monopoles and harmonic bundles. In this talk, we would like to discuss some related topics. We plan to explain equivalences between twisted monopoles and twisted difference modules, generalizing the equivalences in the untwisted case. We also plan to discuss some examples of Higgs bundles to which we may apply our equivalences.