Colloquium abstracts

Takuro Mochizuki
Kyoto University, Japan
March 15, 2018

Periodic monopoles and difference modules:  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.