Variations of Hodge structure and orbits in flag varieties
  Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford-Tate domains, arise as open $G_{\mathbb{R}}$--orbits in flag varieties $G/P$. We investigate Hodge--theoretic aspects of the geometry and representation theory associated with these flag varieties. In particular, we relate the Griffiths--Yukawa coupling to the variety of lines on $G/P$ (under a minimal homogeneous embedding), construct a large class of polarized $G_{\mathbb{R}}$--orbits in $G/P$, and compute the associated Hodge--theoretic boundary components. An emphasis is placed throughout on adjoint flag varieties and the corresponding families of Hodge structures of levels two and four. 
Matt Kerr and Colleen Robles
math.AG math.DG math.RT