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Abstract - In this talk we will introduce generalized hyperpolygons,
which arise as Nakajima-type representations of a comet-shaped quiver,
following recent work with Steven Rayan. After showing how to identify
these representations with pairs of polygons, we shall associate to
the data an explicit meromorphic Higgs bundle on a
genus-g Riemann surface, where g is the number of loops in the comet.
We shall see that, under certain assumptions on flag types, the moduli
space of generalized hyperpolygons admits the structure of a
completely integrable Hamiltonian system. Finally, we shall look into
the appearance of branes within the moduli space of generalized
hyperpolygons as well as of Higgs bundles, and consider mirror
symmetry for such branes. Time permitting, we will mention some other
recent results in various areas of science.