`Periodic monopoles and difference modules'

Abstract:
In 1960's, Narasimhan and Seshadri proved that
a holomorphic vector bundle on a compact Riemann surface
is stable if and only if it is induced by an irreducible unitary
flat bundle. Since then, many generalizations and variants have been
studied. In particular, Simpson proved the equivalence of
irreducible tame harmonic bundles,
stable parabolic bundles with logarithmic connections
and stable parabolic bundles with logarithmic Higgs fields
on compact punctured Riemann surfaces.

In this talk, we shall explain a variant of Simpson's theorem
in the context of periodic monopoles and difference modules,
that is the equivalence between singular periodic monopoles of GCK type
and stable parabolic difference modules.