Variations of Mixed Hodge Structure, Higgs Fields, and Quantum   Cohomology
  Insprired by the work of C. Simpson, it is shown that every variation of graded-polarized mixed Hodge structure defined over Q gives rise to a natural Higgs field on the underlying vector bundle. In the context of Mirror Symmetry it is then shown that these Higgs fields share an intimate relationship with Quantum Cohomology. 
Gregory J Pearlstein