Vincent Koziarz, Université de Nancy, France

Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type

Let g be a lattice in SU(m,1) and let r be a representation of g into the group of isometries of a rank 2 Hermitian symmetric space of non-compact type. Using the correspondence between representations of fundamental groups of Kähler manifolds and Higgs bundles, we will show that the Toledo invariant associated to r satisfies a Milnor-Wood type inequality and we will characterize representations with maximal invariant. This is a joint work with Julien Maubon.