  This brief survey aims to set the stage and summarize some of the ideas under
discussion at the Workshop on Singular Geometry and Higgs Bundles in String
Theory, to be held at the American Institute of Mathematics from October 30th
to November 3rd, 2017. One of the most interesting aspects of the duality
revolution in string theory is the understanding that gauge fields and matter
representations can be described by intersection of branes. Since gauge theory
is at the heart of our description of physical interactions, it has opened the
door to the geometric engineering of many physical systems, and in particular
those involving Higgs bundles. This note presents a curated overview of some
current advances and open problems in the area, with no intention of being a
complete review of the whole subject.
