Wild Harmonic Bundles and Wild Pure Twistor $D$-Modules

The author studies (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, he shows the hard Lefschetz theorem for algebraic semisimple holonomic $D$-modules, conjectured by M. Kashiwara. He also studies resolution of turning points for algebraic meromorphic flat bundles.