The many facets of Higgs bundles

Since their origin in the late 80’s, Higgs bundles manifest as fundamental objects which are ubiquitous in contemporary mathematics and theoretical physics. Some prominent examples of this ubiquity are their role as integrable systems, in Langlands duality and Mirror Symmetry, and in representation theory as character varieties. In this talk we shall give an introduction to Higgs bundles, together with a glimpse of these objects play all the roles mentioned above.