Mirror Symmetry for Higgs Bundles, Generalized Hyperpolygons and More

In this talk we will introduce Higgs bundles and generalized hyperpolygons, and look into different directions that have attracted attention within the area in the last decade.  In particular, we shall see how Mirror Symmetry can be seen in terms of branes within the Hitchin fibration and show that, under certain assumptions on flag types for generalized hyperpolygons, the moduli space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system. Time permitting, we will also see how I have been using my geometric background to answer questions in other areas of science. Much of the talk follows recent work joint with Steven Rayan.