Plática dada por Mark de Cataldo (Stony Brook University, The State University of New York) en el Segundo Congreso Nacional de Geometría Algebraica el lunes 26 de febrero del 2018 Casa Matemática Oaxaca, en Oaxaca de Juárez, México.

Hitchin fibrations are remarkable families of (degenerate) abelian varieties which appear in geometry, arithmetic, representation theory, etc. The study of the singularities of these maps has been the focus of much work, at least since Ngo's proof of the fundamental lemma. One way to encode some of these singularities is to look at the summands appearing in the decomposition theorem. In this talk, we focus on the subvarieties of the target of the Hitchin map that support such summands. I will report on work in progress with J. Heinloth and L. Migliorini in the case of GL(n).