Hodge theory of the middle convolution
  We compute the behaviour of Hodge data by tensor product with a unitary rank-one local system and middle convolution by a Kummer unitary rank-one local system for an irreducible variation of polarized complex Hodge structure on a punctured complex affine line. We give applications of these formulas to local systems with G_2-monodromy. 
Michael Dettweiler and Claude Sabbah
math.AG math.NT