Wild harmonic bundles and wild pure twistor d-modules

We study (i) the asymptotic behaviour of wild harmonic bundles, (ii) the relation between semisimple meromorphic flat connections and wild harmonic bundles, (iii) the relation between wild harmonic bundles and polarized wild pure twistor D-modules. As an application, we show the hard Lefschetz theorem for algebraic semisimple holonomic D-modules, conjectured by M. Kashiwara. We also study resolution of turning points for algebraic meromorphic flat bundles.