  T. Mochizuki constructs a theory of variations of wild Hodge structure for
which the underlying flat connection can have irregular singularities at
infinity. He extends in this way the correspondence of Corlette and Simpson
between irreducible flat bundles and stables Higgs bundles, taking into account
objects with irregular singularities. As an application, he proves a conjecture
of Kashiwara concerning a generalization of the Hard Lefschetz theorem when the
coefficients are the de Rham complex of a simple holonomic D-module on smooth
complex projective variety.
